If each observation of the data is increased by 5, then their mean
a. remains the same
b. becomes 5 times the original mean
c. is decreased by 5
d. is increased by 5

Solution:

Consider x1, x2, ….. xn as the n observations

Old mean \(\overline{x}_{old}=\frac{\sum_{i=1}^{n}}{n}\) …. (1)

By adding 5 in each observation, new mean becomes

x̄new = (x1 + 5) + (x2 + 5) + …. + (xn + 5)/ n

We can write it as

x̄new = (x1 + x2 + …. + xn) + 5n/ n

So we get

x̄new = \(\frac{\sum_{i=1}^{n}x_{i}}{n}\) + 5 (using equation (1))

x̄new = x̄old + 5

Therefore, their mean has increased by 5.

✦ Try This: If the mean of the observations : x + 5, x + 10, x + 15, x + 20, x + 25 is 10, the mean of the last three observations is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.1 Problem 14

If each observation of the data is increased by 5, then their mean a. remains the same, b. becomes 5 times the original mean, c. is decreased by 5, d. is increased by 5

Summary:

In statistics, the mean for a given set of observations is equal to the sum of all the values of a collection of data divided by the total number of values in the data. If each observation of the data is increased by 5, then their mean is increased by 5

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