‘OcIvE CURVE: \wmen cumulative frequencies are pleted on @ graph, then the frequency curve obtained is ‘caled“Ogive" or “Cumulative frequency curve’ “The class limits are shown along the X-axis and cumulative frequencies along the Y-axis. In ‘drawing an ogWve, the cumulatve frequency is ploted atthe upper limit ofthe class Interval The successive points ae late joined tgetyer o get an opve curve. There ae two methods of constuctng ove, — mcr mem] [ae] (Jon +} ees] | «jammer (ch at (cf) cy an In toss than ocive, he less than cumulative frequencies are plotted against upper cass boundaries ofthe respective asses. Then the point i jeined by a smooth fee hand curve and has the shape of en elongated S, MORE THAN OGIVE: {In more than ogive, the mere than cumuaive fequences are plated agains! the lower-class boundaries of he cespectve classes. Then the points are joined by a smooth free hand curve and have the appearance ofan elongated S, upside down, ee APPLIED STATISTICS IN PHYSICAL EDUCATION More than cf SUS SEBEESHISTOGRAM: ‘One of the most important and useful methods of presenting frequency dstbution of Continuous series in known as histogram, In this, the magnitude ofthe class interval is ploted along the horizontal axis and the frequency (on the vertical axis. Each class has lower and upper values and this will give two vertical lines representing the frequency. Histogram is also known as ‘block diagram’ or ‘staircase chart Goals scored [19-15 1547, 1719 19.21 24-28 Number of | 10, 7 6 5 3 footbal players SS APPLIED STATISTICS IN PHYSICAL EDUCATION Number of football players 6 6 re 2 ial 10 °,0 t o’ : 6 tes ia 3 re2 0 ms says oats scored FREQUENCY POLYGON: ‘A grouped frequency dlsinbution can be represented by a histogram. A simple method of ‘smoothing the histogram is to draw a frequency polygon. This is done by connecting the mi point of the top of each rectangle with the mid-point of the top of each adjacent rectangle, by straight lines ‘Mode can easily be found out ‘Goals scored 1315 [tsa arie (| t92t 2123 Number offeotbas | 10 7 6 5 3 players ‘Number of football was say ag asa Goats scored£y eliminating the lowest 25% and the highest 25% of tems ina series, the central 50% values which are ordinarily free of extreme values is known as quartile deviation. To obtain quartile deviation half ofthe distance between the frst and the thiré quartiles is calculated, whichis also known Inter Quartile Range’ Quartile deviation (QD) = (a3-01)/2 CCoetciont of quarile deviation = (3-01) /(23+a1) ‘Semi For symetical dsbuon sores, Q2=CO*Masan _isMedan-0D Monts 1 Ri ipl founrtand nd eon compte 2, Renal inuencd byte exome vale, 3. ean be foun ou wih open end dato, 4. hs nat tec he presence of ero tas i APPLIED STATISTICS IN PHYSICAL EDUCATION Demet 1. Rignores the frst 25% ofthe items and the last 25% of the items, 2. tis postional average, hence not amenable to further mathematical treatment. 3. Its value is affected by sampling fuctuations, 4, Ikgves only @ rough measure, ‘Mean Deviation: ‘Mean deviation is the arithmetic mean of the daviations of a series computed from any ‘measure of central tendency, je, the mean, median or mode. All deviations are taken as positive i ++or—signs are ignored. Mean deviation is denoted as 8 (Det) ‘Mean ceviaton is the average amount of scater ofthe tems ina cistbuton from either the ‘mean or the median, ignoring the signs of the deviation ~ Clark and Schekade Mean deviation = 50 ANI CCoefcint of mean deviation = Mean deviation mean or median or mode Merits: 1. tis simple to understand and easy to compute, Mean deviation is a calculated value. 2. tis not much affected by the fuctuations of sampling 3. It's based on all tems ofthe series and gives weight according to their size. 4, kis less affected by the extreme items. 5. this rigidly defined. 6. tis exible because it can be calculated from any measure of central tendency. 7. kis better measure for comparison, Demerits: Itis non-algebraic treatment, Algebraic positive and negative signs are ignored. IRis not a very accurate measure of dispersion. Itis not suitable for further mathematical calculation. tis rarely used. ‘Standard Deviation:‘MEASURE OF CENTRAL TENDENCY ‘A measure of central tendency isa single value that attempts to describe a set of daa by identifying the central position within that et of data. As such, measures of central tendency ae sometimes called measures of central Tocation. They are also classed as summary statistics, The mean (often called the average) is most likely the ‘measure of central tendency that you are mos familiar with, but there are others, such a the median and the mode. “Tho mean, median and mode are all valid measures of central tendency, but under diferent conditions, some measures of central tendency become more appropiate rouse shan eters. Inte following sections we will look atthe mean, mode and median, and lean how to ealulate them and under what conditions they are most appropriate to be use. “0 Mean In dhe most layman terms, Mean is defined asthe sum ofall the observations divided by the ttal number of cbservations. The above definition i of Aritumetic Mean, one of the many types of Mean In deal. he types of ‘mean are explained although most of them are out of scope for elementary Statistics 1: Arithmetic Mean ‘Arithmetic Moan is the average of all he observations. Generally ifthe mean is mentioned without any adjective, itis assumed to be Arithmetic Mean, Example: We havea set of observatons-x=1.35,7.91,35:7.9. The Arithmetic Mean is computed as (xin) where {the numberof observations which is equal tS in this case. This x-25 in this case and n=5 so the mesn comes cut tobe Median “The median isthe mile score frase of data that hes been aranged in order of magnitude. The medians less flected by outliers and skewed data In order to ealeulate the median, suppose we have the data below: (ese tsps pe [ss epee | Weis ned to rearange tat data into oder of magne (mallet firs ‘Our median matk is the middle mark - in this eas, 56 (highlighted in bold). Its the middle mark because there are 5 score efore i and 5 scores afer it. This works fine when you have an odd number of sores, bu what happens when you have an even number of sores? What if you had only 10 scones? Well, you simply have to take the middle to scores and average the result. So if we look at the example below: Ses ee as ee aa ‘We again earrange tat daa into order of magnitude smallest fi: OSs see on ow we have to take the Sth and 6th score in our data set and average them to get a median of $35. Mode ‘The mole isthe mort frequent score in our data set.Ona histogram it represents the highest bat ins bar chart or histogram. You can, therefore, sometimes consier the mode as being the most popular option. An example ofa ‘mode is presented below: 2030 40.4060 12.40 othe score repeated maximum number of time wil be taken ss mode. Its 40 “ 2. Measure of variability ‘Variability is most commoaly measure with the following descriptive statistics: Range: the difference between the highest and lowest values. Iterquarile range: the range ofthe middle half of a distribution, Standard deviation: average distence from the racea.‘Standard Deviation: Karl Pearson introduced the concept of standard deviation in 1893. It is the mostimportant measure of dispersion and is widely used in many statistical formulas. Standard deviation is also {=} Y.M.C.A. COLLEGE OF PHYSICAL EDUCATION called ‘Root-Mean Square Deviation’ or ‘Mean Error’ or ‘Mean Square Error’. Standard deviation is defined as positive square-root of the arithmetic mean of thesquares of the deviations of the given observation from their arithmetic mean. The standard deviation is denoted by o (Sigma). Standard deviation indicates the spread of the middle 68.26 percent of scores taken from the mean. Merits: weer aww It is rigidly defined, and its value is always definite and based on all the observations andthe actual signs of deviations are used. . As itis based on arithmetic mean, it has all the merits of arithmetic mean. Itis the most important and widely used measure of dispersion. It is possible for further algebraic treatment. Itis less affected by the fluctuations of sampling, and hence stable. . Squaring the deviations make all of them positive, there is no need to ignore the signs. It is the basis for measuring the coefficient of correlation, sampling and statisticalinferences. . The standard deviation provides the unit of measurement for the normal distribution. It can be used to calculate the combined standard deviation of two or more groups. Demerits: “ere It is not easy to understand, and it is difficult to calculate. It gives more weight to extreme values because the values are squared up. Itis affected by the value of every item in the series. . As it is an absolute measure of variability, it cannot be used for the purpose ofcomparison.