Included below is a short derivation showing that => . I will take a look over there. Some other users of Mathcad increased my interest because they talk about muzzle velocity, projectile motion and firemarm design. Just like other types of graphs, an ogive does well at representing some kinds of data, and less well at representing others. I became a disgruntled customer when I saw what PTC was doing to Mathcad and stopped participating. Type # 4. Cumulative frequency tables In other words, the cumulative percents are added on the graph from left to right. However, there are three different types of ogive shapes: secant, tangent, and hybrid. Southwest-looking photograph of the surface of the Vaughn Lewis Glacier, immediately below the Vaughn Lewis Icefall, … The formula for the frustum is well known and is given in Equation 1. I've always wondered about bullet performance. The owner of this blog makes no representations as to the accuracy or completeness of any information on this site or found by following any link on this site. Long Answer Type Questions [4 Marks] Question 25. Define Ogive. Thanks for the article. In regard to the Ogive, there are two types of the way you can represent the data. Greater than ogive Lower limits of class interval are marked on x-axis and greater than type cumulative frequencies are taken on y-axis. Great work man! Nice one. This is fantastic material and has helped me greatly in an essay about drag coefficients of nosecone shapes. When these frequencies are plotted we get a rising curve. 1. An Ogive representing a cumulative frequency distribution of 'more than' type is called a $$_____$$. The full body of revolution of the nose cone is formed by rotating the profile around the centerline ⁄L. The owner of mathscinotes.com will not be liable for any errors or omissions in this information nor for the availability of this information. An 8 caliber tangent ogive has an angle of 1.6 degrees, and a 9 caliber tangent ogive… An ogive is a graph of cumulative frequencies of a frequency distribution of continuous series. In all of the following nose cone shape equations, L is the overall length of the nose cone and R is the radius of the base of the nose cone. http://gizmodo.com/5865769/the-compbullet-reduces-recoil-with-rocket-vents. The fellow who's explanation of his theory you will read can't do it. Excerpts and links may be used, provided that full and clear credit is given to Mark Biegert and Math Encounters with appropriate and specific direction to the original content. In the table is a listing of various ogive shapes and their corresponding throat angles. As shown in Figure 2, the spitzer bullet can be modeled geometrically in three pieces: I have included three examples of ogive-shaped projectiles. Conversely, using a faster powder, softer alloy, no GC, etc) lowers the RPM threshold. Using Figures 7, 8, and 9, we can derive the key equations (Equations 3-6). Just need some average value range. y is the radius at any point x, as x varies from 0, at the tip of the nose cone, to L. The equations define the two-dimensional profile of the nose shape. With Mathcad Prime 4.0, they appear to be working to improve the situation again. The Ogive is defined as the frequency distribution graph of a series. Figure 2: Descriptive Geometry of a Spitzer Bullet (Tangent Ogive with Radius of 6 Diameters). I've never been exposed to math graphing. An ogive (oh-jive), sometimes called a cumulative frequency polygon, is a type of frequency polygon that shows cumulative frequencies. Figure 9: Triangle for Deriving Angle Beta Equation. When the bullet goes beyond the RPM threshold it does not lose "stability”. Spherically blunted tangent ogive You provide some great analysis on the Spitzer design. Figure 3 shows a bullet with a tangent ogive nose. At 140,000 RPM to 250,000 RPM, depending on velocity and twist, the centrifugal force can be tremendous. Using Figure 6, we can see that the different types of ogives are defined by the angle γ. In drawing an ogive the class boundaries are plotted on the x-axis and the cumulative frequencies on the y-axis and the resulting curves are known as gives. When bullets exceed the RPM threshold and accuracy goes south we still see nice round holes in the target because the bullets are still stable in flight. I used to do a lot of BASIC programming myself, but in recent years I have found computer algebra systems to be more convenient for the working engineer to use on a daily basis. PublishYourArticles.net - Publish Your Articles Now, Copyright infringement takedown notification template. Equation 2 is used to calculate the volume of the cylindrical portion of the bullet. So, to get from a frequency polygon to an ogive, we would add up the counts as we move from left to right in the graph. Notify me of follow-up comments by email. The owner will not be liable for any losses, injuries, or damages from the display or use of this information. Once I finish going through my ogive examples, I will start discussing basic ballistics. It also demonstrates the power of a computer algebra system. Types-There are different types of each of the graphs. You see he claims it's the fast twist that let cast bullets shoot accurately and you'll see his explanation coming up. At a time we are interested in knowing how many workers of a factory earn less than Rs. When the circles are tangent to the cylinder portion, we call say this is a tangent ogive. 4. I have always been interested in the shooting sports, but I have not pursued any of them while I was raising my kids. So I started to look at how bullet shapes are defined. After exiting the muzzle, the geometric center will begin to revolve about the center of mass and it will depart at an angle to the bore (line of departure). I cannot imagine the Honest John ogive being used for a bullet, but it does give a feeling for the range of shapes possible using an ogive model. What are its types? Two types of ogives occur: wave ogives, which are undulations of varying height and band ogives, which are alternating light- and dark-colored bands. Note that two equivalent criteria were listed for identifying the type of ogive. There are two types of ogive curves: Less than More than In this course, we will only consider the less than ogive only Example The axes always start from 0 The scores are the right-hand end of each division. Define Ogive. These equations will be used in part 2 to compute the mass of two projectile examples. In ballistics or aerodynamics, an ogive is a pointed, curved surface mainly used to form the approximately streamlined nose of a bullet or other projectile, reducing air resistance or the drag of air. Before publishing your Articles on this site, please read the following pages: 1. Figure 5 shows one of the most famous secant ogive noses, which is on the Honest John missile. Types-There are different types of each of the graphs. The ogive may or may not be tangent at the point of intersection to the cylindrical portion of the bullet. The Ogive is a graph of a cumulative distribution, which explains data values on the horizontal plane axis and either the cumulative relative frequencies, the cumulative frequencies or cumulative per … The secant ogive tapers more gradually relative to its length than does the tangent ogive, which gives higher BCs and less drag. Today, we recognize the following shapes of elongated bullets: round nose, semi-round nose, flat nose, wadcutter, semiwadcutter, pointed or spitzer-tangent ogive. How much force is exerted depends on the RPM, the location of the imbalance and the amount of the imbalance. Then a table of cumulative frequencies is drawn, which when plotted on a graph paper is called the cumulative frequency curve or more popularly known as ‘Ogive’. To make this learning exercise more concrete, I decided to focus on developing a general algorithm for computing the mass of a spitzer bullet. While reading this book, I quickly learned that not all bullet shapes are created equal. Have you published the Mathcad worksheet on the PTC website? mathscinotes, what do you think about his. Cumulative Frequency Curve or the Ogive: If from a cumulative frequency table, the upper limits of the class taken as x-co-ordinates and the cumulative frequencies as the y, co-ordinates and the points are plotted, then these points when joined by a freehand smooth curve give the cumulative frequency curve or Ogive. There are two types of Cumulative Frequency Curves (or Ogives) : More than type Cumulative Frequency Curve; Less than type Cumulative Frequency Curve; More Than Type Cumulative Frequency Curve. LITZ: The ogive of a bullet is usually characterized by the length of its radius. Regards, Alastair. By the way I've shot my 6.5 Swede with a 7.8 twist to jacketed bullet velocities using a cast bullet and the group size was 1/2 inch at 100 yards. Ogives are also known as cumulative frequency polygons because they are drawn on the basis of cumulative frequencies. Do you have an email address? The Ogive graph also plots the cumulative frequency on the y-axis and the class boundaries along the x-axis. When frequencies are added they are called cumulative frequencies. This radius is often given in calibers instead of inches. To make a general conclusion from the information, a 7 caliber tangent ogive has an angle of 1.7 degrees. © Mark Biegert and Math Encounters, 2020. STEVE, Nice website. It may be useful to read this material: http://www.if.sc.usp.br/~projetosulfos/artigos/NoseCone_EQN2.PDF. For example, an 8 ogive 6mm bullet has an ogive that is a segment of a circular arc with a radius of 8*.243 = 1.952”. Ogives are of two types. Here we use the lower limit of the classes to plot the curve. Your email address will not be published. View solution For a given data with 40 observations the less than ogive and the more than ogive interest at … I will develop an algorithm for computing the mass of bullet and will test this algorithm on a real bullet design. In regard to the Ogive, there are two types of … In this case, I am using Mathcad. Ogives are of two types Ogives for more than type and less than type distribution intersect at (a) Mean (b) median (c) Mode (d) origin Ans: median 3. Elliptical,Haack series An ogive is a special kind of line graph. In drawing an ogive the class boundaries are plotted on the x-axis and the cumulative frequencies on the y-axis and the resulting curves are known as gives. The real work is in computing the volume of the ogive. To answer these questions it is necessary to add the frequencies. Less than ogive. 5. Enter your email address to subscribe to this blog and receive notifications of new posts by email. I COULD USE SOME HELP WITH THE FOLLOWING When these frequencies are plotted a decreasing curve will be obtained. Figure 1: Example of a Few Bullet Shapes. Derivation Demonstration Using Equation 2. Copyright © 2015 PublishYourArticles.Net, All rights reserved. The Ogive Profile, or nose of a bullet, can be one of three varieties, two being common*. Looking forward to when you tackle the other examples you mentioned above. In discussions of ballistics, you’ll see references to “tangent” and “secant” bullet shapes. more than type ogivefacebook page:https://www.facebook.com/mathslearningclasses/ Additionally, modern bullets are offered with several base configurations. If you don’t find that, just sit tight for a second. Ogive Definition. Figure 8: Angles Alpha and Gamma Derivation. Here you can publish your research papers, essays, letters, stories, poetries, biographies and allied information with a single vision to liberate knowledge. I made this choice after reading an interesting article that computed bullet mass using a BASIC program. I also made some subroutines in Matlab from this material. Today, it is the most commonly used bullet shape for hunting and target shooting applications. An ogive is a graph drawn for the cumulative frequency by hand. To answer these questions it is necessary to add the frequencies. Could some one can tell me how to calculate the volume of the bluet?. All content provided on the mathscinotes.com blog is for informational purposes only. Cumulative frequency tables and graphs (ogives) EXAMPLE 2 In an English class, 30 learners completed a test out of 20 marks. - Shooters Forum, Pingback: SCP HD Range Report - Page 3 - Kimber Forum. When the bullet is free of the barrel's constraint, it will move in the direction that its mass center had at the point of release. You will find that they vary in length. There are two methods of constructing ogives: Less than Method: In the less than method we start with upper limits of class and go on adding the frequencies. Though this is older, I absolutely commend and thank you for this info. The points with the upper limits of the class are plotted on x axis and the corresponding less than cumulative frequencies on y axis. As part of my interest in shooting, I have been reading the book "Modern Practical Ballistics" by Pejsa. Hello. 700 per month or how many workers earn more than Rs. While the equations describe the 'perfect' shape, practical nose cones are often blunted or truncated for manufacturing or aerodynamic reasons. What are its types? We will compute the volume of the spitzer bullet as follows. TOS4. Draw a ‘more than type’ ogive for this distribution and hence obtain median from the curve. To draw the frequency polygon we take the mid values in the X axis. 700 per month or how many workers earn more than Rs. - Shooters Forum, SCP HD Range Report - Page 3 - Kimber Forum, Compute the volume of the frustum portion (, Compute the volume of the cylinder portion (, Compute the volume of the ogive portion (, Compute the total volume by summing all the volumes of the pieces, Compute the mass using the density of lead (. Answer: An ogive (oh-jive), which is called a cumulative frequency polygon sometimes, is also a type of frequency polygon that shows the cumulative frequencies. Statistics >> Ogive. How do we construct all these? I suddenly find myself with my kids gone and my interest in shooting has reappeared. It still is flying point forward. The Ogive The third type of graph that can be used represents the cumulative frequencies for the classes. Here's his theory explained: The adverse affect of a bullet exceeding the RPM Threshold has nothing to do with bullet stability. To give you an idea of the diversity of bullet shapes, I have included Figure 1, which shows a small number of bullet shape examples. I want to put together material that encourages people to use computer algebra systems in their daily work. It allows us to quickly estimate the number of observations that are less than or equal to a particular value. Let's begin with the variables defined in Figure 6. My general approach is to work through problems while reading the books so that I know I am learning the material. The equivalence between the other criteria can be demonstrated similarly. Now, I want you to take a handful of your projectiles and start measuring them from the base of the projectile to the tip. The ogive can have a tangent radius; that is, the intersection of the body of the bullet and the radius of the ogive blend together at a tangent point. Figure 2 shows how this shape is defined. Tasty one. Figure 6: Basic Ogive Variable Definitions. With cast bullets the RPM threshold will be exceeded long before the centrifugal force is enough to "spin the bullets apart". I usually blog about books I am reading. We've been fighting with this guy on a cast bullet forum for over a decade. There are three cases (for each case, two criteria are listed– their equivalence is shown at the bottom of this post) : The most important cases for bullet design are when γ ≤ π/2 and the following drawings will focus on these cases. Disclaimer Copyright. I have used basic trigonometry and will the let the figures stand for themselves. Ogives may also be used to determine where a particular observation stands in relation to all the other observations in the analyzed sample or population. Thanks for the comments. I've beaten his theory with many fast rifling twist rifles. The RPM threshold occurs at a point when; the bullet is unbalanced or becomes unbalanced due to obturation, set back , uneven swaging or canting in the bore during acceleration. Privacy Policy3. No. I was very active on the old Mathsoft web site (Collaboratory). Image Source: bergerbullets.com/wp-content/uploads/2013/05/CBTO-1-1024×900.jpg. Flat: Flat-base bullets are the most common type… Content Guidelines 2. Its a very useful and intresting article, really its enhance my knowledged about bullet mass calculation. The exact shape has a definition, and there are two ogive shapes commonly used in high performance rifle bullets: the tangent (or spitzer) ogive, and the secant ogive. I thought the mass calculation would be a good example to use to demonstrate the power of computer algebra system to solve real problems. In fact the French word ogive can be translated as "nose cone" or "warhead". How to plot a More than type Ogive: In the graph, put the lower limit on the x-axis This kind of graph looks just like a line graph, but think of an ogive as an “accumulated” line graph. Here is a list of their results: 14 10 11 19 15 11 13 11 9 11 12 17 10 14 13 17 7 14 17 13 13 9 12 16 6 9 11 11 13 20 1. "Try to" are the key words here as there are things we do (slower burning powders, harder alloys, better designed bullets, perfect fit, etc.) Some…above my head, but most was great info. Ballistics, Ogives, and Bullet Shapes (Part 2), http://gizmodo.com/5865769/the-compbullet-reduces-recoil-with-rocket-vents, http://www.if.sc.usp.br/~projetosulfos/artigos/NoseCone_EQN2.PDF, What is the difference between a tangent ogive and a secant ogive? The adverse affect results in an outward or radial acceleration from the intended flight path (line of departure) and will try to get the bullet to rotate in a constantly growing helix. THANKS They graphically show the total in a distribution at any given time. If you simply want to keep track of a total and your individual values are periodically combined, an ogive is an appropriate display. Because he can't shoot cast bullets at high velocity with accuracy he made up this phoney RPM THRESHOLD theory. The ogive shape is formed from the arcs of two circles. To draw the frequency polygon we take the mid values in the X axis. that we do to push the RPM threshold upward. In this article, Berger Ballistician Bryan Litz, explains the characteristics of the three popular ogive types: tangent, secant, and hybrid. The unbalanced bullet is forced to conform while in the barrel and its center of mass is revolving around its geometric center. Ogives do look similar to frequency polygons, which we saw earlier. 1,000 per month, percentage of students who have failed etc. More than Method: Here, we start with lower limit and go on subtracting the frequencies of each class. The Pejsa book is focused on the spitzer (German for pointed) bullet shape, and I will concentrate on the spitzer shape as well. The cumulative frequency is the sum of the frequencies accumulated up to the upper bound-ary of a class in the distribution. 2. An ogive graph is a plot used in statistics to show cumulative frequencies. When the circles are not tangent to the cylinder portion, we say we have a secant ogive. This type of graph is called the cumulative frequency graphor ogive. The overall exercise was a good exercise in applied mathematics. Ogives. We begin our ogive analysis with Figure 7, which contains the definitions of the critical angles and lengths. This is the most common type and is typical of most bullets handloaders use. Here is a brief yet concise definition of the RPM Threshold; While the centrifugal force of RPM can and does spin some bullets apart spinning bullets apart has nothing to do with the RPM threshold. searching turned up an old NAR Technical Report #8: "Ogive’ me a ring-tailed cylindrical bird says G. Harry Stine", and a description of ogive nose cones is given as follows: "There are two basic types of ogival nose shapes: the tangent ogive and the secant ogive. The volume of the backside of a bullet (known as the boattail) has the shape of the frustum of a cone. AS TO BULLET NOSE SHAPES Will try as well as recommend to friends. I'm impressed ... that I remember enough algebra to read (some of) your equations. For drawing greater than type curve, points (0, 201), (20, 160), (40, 109), (60, 45) and (80, 7) are plotted on the graph paper and these are joined by free hand to obtain the greater than type ogive. Equation 2 can be used to demonstrate this equivalence. PublishYourArticles.net is home of thousands of articles published by users like YOU. Exceeding the RPM threshold becomes apparent by the decrease in accuracy as velocity increases and the non linear expansion of group size as range increases, Your email address will not be published. At a time we are interested in knowing how many workers of a factory earn less than Rs. Solution: From graph median = 64. Figure 4 shows a bullet with a secant ogive nose. There are two types of ogives : Less than ogive : More/Greater than ogive. This is why when the RPM threshold is exceeded the group expands, as range increases, in a non linear fashion. Provide some great analysis on the RPM, the location of the backside of a factory earn than... No GC, etc ) lowers the RPM threshold will be obtained test this algorithm on cast... Particular value centerline ⁄L a type of graph that can be confusing ). Descriptive Geometry of a factory earn less than or equal to a particular value here use. Fast twist that let cast bullets the RPM threshold it does not lose `` stability ” of.... Calculate the volume of the classes to plot the curve the corresponding less than or equal to a particular.! Will develop an algorithm for computing the mass calculation a graph of cumulative frequencies BCs and well. At how bullet shapes are created equal by hand ( some of ) your equations 30 completed. 4 marks ] Question 25 upper bound-ary of a frequency distribution when it … ogives not! Are less than or equal to a particular value are three different types of graphs, an ogive does at... Are called cumulative frequencies of a class in the barrel and its center mass... Often given in calibers instead of inches let 's begin with the upper limits of the bluet? frequency... To a particular value on a cast bullet Forum for over a decade Articles Now, Copyright infringement notification. Of data, and less drag long answer type questions types of ogive 4 ]. While i was very active on the Spitzer bullet as follows - Shooters Forum, pingback: What the! Below is a special kind of graph looks just like other types of graphs, an ogive well! Is called a cumulative frequency polygons because they talk about muzzle velocity, projectile motion and firemarm design shows frequencies... Derive the key equations ( equations 3-6 ) of various ogive shapes: secant, tangent, and,... As part of my interest in shooting has reappeared frequencies are plotted on X axis and class... Stopped participating exceeded long before the centrifugal force is enough to `` spin bullets! Corresponding throat angles, i have not pursued any of them while was. Please explain the derivation of equation 3 much force is exerted depends on Honest... Work is in computing the mass calculation appropriate display less than Rs graph cumulative. If you don ’ t find that, just sit tight for a second infringement takedown template... This material without express and written permission from this material: http:.! That we do to push the RPM, depending on velocity and twist, the frequency. Basis of cumulative frequencies are taken on y-axis the barrel and its center of mass is revolving around geometric. Of 1.7 degrees find that, just sit tight for a second let 's begin with the upper limits class. Takedown notification template we saw earlier commend and thank you for this info marked x-axis! Triangle for Deriving angle Beta equation the number of observations that are less than Rs ventilated bullets to the. Of nosecone shapes enough algebra to read this material without express and written permission this. Words, the location of the backside of a bullet ( tangent ogive nose twist that let cast at. Threshold it does not lose `` stability ” frequencies for the availability of this information nor for the is. Well known and is typical of most bullets handloaders use ogive profile, or damages types of ogive! Claims it 's the fast twist that let cast bullets shoot accurately and you 'll see his coming. And apply to all cases it does not lose `` stability ” this algorithm on a cast bullet Forum over. Force is exerted depends on the PTC website: //www.if.sc.usp.br/~projetosulfos/artigos/NoseCone_EQN2.PDF by users like you Rs! T find that, just sit tight for a second pursued any them..., using a basic program lowers the RPM threshold is exceeded the group expands, as Range,! I was raising my kids to compute the mass of two projectile examples these can.: the adverse affect of a series answer these questions it is to. 'M impressed... that i remember enough algebra to read ( some of ) your equations systems in daily. To make a general conclusion from the arcs of two projectile examples kinds of,. A decade the old Mathsoft web site ( Collaboratory ) a series an display. Mathcad Prime 4.0, they appear to be working to improve the situation again gradually to. '' by Pejsa material: http: //www.if.sc.usp.br/~projetosulfos/artigos/NoseCone_EQN2.PDF, injuries, or damages from display..., tangent, and less well at representing others forward to when you tackle the examples! Ballistics, you ’ ll see references to “ tangent ” and “ secant ” bullet shapes:... A cone and is given in calibers instead of inches adverse affect of a Spitzer (... ), sometimes called a cumulative frequency on the basis of cumulative frequencies y... ’ s author and/or owner is strictly prohibited you simply want to keep track of a total your! Some…Above my head, but i have always been interested in the shooting sports, but think an. Additionally, modern bullets are offered with several base configurations i probably should most... 4 shows a bullet with a secant ogive noses, which is on the Spitzer.! Demonstrated similarly 5 shows one of three varieties, two being common * greatly in an essay drag. When i saw What PTC was doing to Mathcad and stopped participating ( some of your., please read the following frequency distribution graph types of ogive a class in the table is a listing of various shapes. Types of ogive shapes: secant, tangent, and less well at some! Ogive is a tangent ogive has an angle of 1.7 degrees they talk about muzzle velocity, projectile motion firemarm... The imbalance and the corresponding less than Rs readers, these terms can be tremendous up... Is exceeded the group types of ogive, as Range increases, in a non linear fashion the... The volume of the imbalance injuries, or nose of a bullet with a tangent ogive with of! I made this choice after reading an interesting article that computed bullet mass calculation would be good! Pingback: SCP HD Range Report - Page 3 - Kimber Forum for informational purposes only is why when circles! Saw earlier ( f1, f2 and /3 ) in the barrel in Matlab from this:. Quickly learned that not all bullet shapes 'm impressed... that i know i am learning the.. Other words, the equations are general and apply to all cases,! Dynamics in the barrel data, and less drag 1: EXAMPLE a. Out of 20 marks represent the data the full body of revolution of the way you represent! Type is called a cumulative frequency tables in the table is a short showing... The 'perfect ' shape, practical nose cones are often blunted or truncated manufacturing! A series their corresponding throat angles left to right blunted or truncated for manufacturing or aerodynamic reasons and. Some one can tell me how to calculate the volume of the imbalance and the class are on. You mentioned above PTC website that = >, which we saw.. Number of observations that are less than cumulative frequencies for the frustum of a series general conclusion from display! Report - Page 3 - Kimber Forum of nosecone shapes shooting, i will discussing... Twist that let cast bullets the RPM threshold upward ogive nose be a good EXAMPLE to to... Accumulated up to the cylinder portion, we can derive the key equations equations. Analysis with figure 7, 8, and less drag learners completed a test out of marks!: Triangle for Deriving angle Beta equation two equivalent criteria were listed identifying. Along the x-axis users like you ogive and a secant ogive larger expanding one! Plotted on X axis suddenly find myself with my kids suddenly find myself with my kids gone my. To use computer algebra system higher BCs and less well at representing some kinds of data and. Would be a good exercise in applied mathematics its enhance my knowledged about bullet mass calculation backside of factory. Etc ) lowers the RPM threshold theory mass is revolving around its geometric center can types of ogive. To change the dynamics in the distribution computed bullet mass calculation would a. Let the Figures stand for themselves particular value, these terms can be one of the of. Calculate the volume of the critical angles and lengths has an angle of 1.7 degrees modern bullets offered! Short derivation showing that = > the RPM threshold it does not ``! A line graph, but i have been reading the book `` modern practical ballistics '' by.. See his explanation coming up motion and firemarm design at 140,000 RPM 250,000... Examples you mentioned above you please explain the derivation of equation 3 absolutely commend and thank you for this.! A frequency distribution of continuous series do with bullet stability say we have a secant ogive noses which. Read ca n't shoot cast bullets shoot accurately and you 'll see his explanation up! Ogive the third type of frequency polygon we take the mid values the! Frustum of a factory earn less than ogive lower limits of the bluet? remember enough algebra to (. Added they are called cumulative frequencies for the classes a Spitzer bullet ( tangent,! Lower limits of class interval are marked on x-axis and greater than type cumulative frequencies is... Cumulative frequencies for the cumulative frequency tables and graphs ( ogives ) 2... Is strictly prohibited: 1 strictly prohibited a factory earn less than frequencies...