Q9 of 33 Page 156

Marks of 12 students in a unit test are given as 4, 21, 13, 17, 5, 9, 10, 20, 19, 12, 20, 14.

Assume a mean and calculate the arithmetic mean of the data. Assume another number as mean and calculate the arithmetic mean again. Do you get the same result? Comment.

Given, observations are 4, 21, 13, 17, 5, 9, 10, 20, 19, 12, 20, 14


Let assumed mean, a = 17


We know, mean by assumed mean method is



Where, a is assumed mean and n is no of observations and xi's are observations.


Therefore, mean for given data





Now, let assumed mean a = 14





Yes, we get same result in both cases !


This shows that, actual mean doesn't depend on assumed mean !


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Find the sum of deviations of all observations of the data 5, 8, 10, 15, 22 from their mean.

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If sum of the 20 deviations from the mean is 100, then find the mean deviation.

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Arithmetic mean of marks (out of 25) scored by 10 students was 15. One of the student, named Karishma enquired the other 9 students and find the deviations from her marks are noted as − 8, − 6, − 3, − 1, 0, 2, 3, 4, 6. Find Karishma’s marks.

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The sum of deviations of ‘n’ observations from 25 is 25 and sum of deviations of the same ‘n’ observations from 35 is − 25. Find the mean of the observations.