First slide

Introduction to statistics

Question

. If the sum of deviations of a number of observations about 4 is 30 and that about 3 is 40. Then, mean of the observations is

Moderate

A

7
B

10
C

11
D

None of these

Solution

Given that, $\sum_{i = 1}^{n} (x_{i} - 4) = 30$
and $\sum_{i = 1}^{n} (x_{i} - 3) = 40$
i.e.., ${Σx}_{i} - 4 n = 30$ (i)
and ${Σx}_{i} - 3 n = 40$ ..(ii)
On solving Eqs. (i) and (ii), we get
$\begin{aligned} n = 10 and {Σx}_{i} = 70 \\ ∴ \sum_{i = 1}^{n} x_{i} \end{aligned} Mean = \frac{1}{10} (70) = 7$

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