Mathematics

Mean, median and mode are three measures of central tendency. Mean of the grouped data is calculated by using the following methods: (a) Direct method (b) Assumed mean method (c) Step deviation method Mode is that value of the observation which occurs most frequently. If data has more than one value of the same maximum frequency, it is said to be multimodal. In grouped frequency distribution, the class with maximum frequency is called modal class. The mode is the value inside the modal class and is calculated by using the following formula. Mode = l + {(f1–f0) / (2f1-f0-f2) }h, where l = lower limit of the modal class, h = size of the class interval (assuming all class sizes to be equal), f1 = frequency of the modal class, f0 = frequency of the class preceding the modal class, f2 = frequency of the class succeeding the modal class. Median is the value of the middle-most observation in the data. To find the median of a grouped data, first find the median class and then use the following formula: Median = l + h {(n/2–cf)/f}, where l = lower limit of median class n = number of observations cf = cumulative frequency of class preceding the median class f = frequency of median class h = class size The empirical relationship of median with other two measures of central tendencies can be written as: 3 Median = Mode + 2 Mean The cumulative frequency of a class can be obtained by adding the frequencies of all the classes preceding the given class. Cumulative frequency distributions can be represented graphically by a cumulative frequency curve (also known as ogive). There are two types of ogives namely ‘less than’ ogive and ‘more than’ ogive. Median can be found after drawing the cumulative frequency curves by two methods. I. After drawing one of the ogives, find a point corresponding to n/2 on y-axis. From this point, draw a line parallel to the x-axis cutting the curve at a point. The abscissa of this point gives the median of the data. II. After drawing both ‘less than’ and ‘more than’ ogives, find the abcissa of their point of intersection. This point gives the median of the data. Keywords: Statistics

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