First slide

Introduction to statistics

Question

In a set of 20 observations, each of the observation below the median of all observations is increased by 6 and each of the remaining observation is decreased by
2.Then the mean of the new set of observations

Moderate

A

increase by 1
B

decrease by 1
C

increase by 4
D

increase by 2

Solution

Arrange all observations in increasing or decreasing
order.
Let the observations be $x_{1}, x_{2} \dots x_{20}$ so that ${\frac{x_{10} + x_{11}}{2}}_{}$ .is the
median. The new set of observations will be $x_{1} + 6, \dots x_{10} + 6, x_{11} - 2, \dots, x_{20} - 2$
Their mean is equal to
$\begin{aligned} \frac{1}{20} (\sum_{i = 1}^{20} x_{i} + 6 \times 10 - 2 \times 10) \\ = \frac{1}{20} \sum_{i = 1}^{20} x_{i} + 2 \end{aligned}$

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