First slide

Introduction to statistics

Question

Mean deviation about mean from the following data:
$\begin{array}{l} x_{i} : 3 9 17 23 27 \\ f_{i} : 8 10 12 9 5, \end{array}$
is

Moderate

A

6
B

7
C

8
D

9

Solution

Calculation of mean deviation about mean.
$x i$ $f i$ $f_{i} x_{i}$ $|x_{i} - 15|$ $f_{i} |x_{i} - 15|$
3
9
17
23
27
8
10
12
9
5
24
90
204
207
135
12
6
2
8
12
96
60
24
72
60
$N = Σ f_{i} = 44 Σ f_{i} x_{i} = 660 Σ f_{i} |x_{i} - 15| = 312$
mean $= \bar{X} = \frac{Σ f_{i} x_{i}}{N} = \frac{660}{44} = 15$
Mean deviation $= M \cdot D \cdot = \frac{1}{N} Σ f_{i} |x_{i} - 15| = \frac{312}{44} = 7.09 ≃ 7$

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