By A. I Markushevich

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**Sample text**

Calculate the average. 0. Calculate the true mean value. 33 Three people A, B, C were given the job of finding the average of 5000 numbers. Each one did his own simplification. A's method. Divide the set into sets of 1000 each, calculate the average in each set and then calculate the average of these averages. B's method. Divide the set into 2000 and 3000 numbers, take average in each set and then take the average of the averages. C's method. 500 numbers were unities. He averaged all other numbers and then added one.

D) Here 7 occurs with frequency 2 and 10 occurs with frequency 3 and others occur with frequency one. If these are represented by a histogram then there will be two peak points corresponding to the frequencies 2 and 3. Hence there are two modes, namely, 7 and 10. This can be called a bimodal data. Comment. According to the definition a given data may or may not have a mode and if it has a mode the mode may not be unique, that is, there can be a number of modes. 2 Calculate the mode, if it exists, for the following data.

Columns 1 and 2 give the data, columns 4 and 6 give the' less than cumulative' and the' greater than cumulative' frequencies respectively. 6 and when the points are connected by straight lines we get a ' less than ogive '. 6 give a ' greater than ogive' STATISTICAL POPULATIONS AND SAMPLING 21 when plotted. It should be noticed that the upper and lower class limits are taken instead of the class marks and the cumulative frequencies are plotted. 2. 46 Pie Diagrams In this representation the frequencies in the various classes are represented by the various sectors of a circle.