First slide

Introduction to statistics

Question

The mean deviation about median from the data 340, 150, 210, 240, 300, 310, 320, is

Moderate

A

50
B

52.8
C

55
D

45

Solution

Arranging the observations in ascending order of magnitude, we have 150, 210, 240, 300, 310, 320, 340. Clearly, the middle observation is 300.
$∴$ Median= 300.
Calculation of Mean Deviation
$x i$ $|d_{i}| = |x_{i} - 300|$
340
150
210
240
300
310
320
40
150
90
60
0
10
20
Total $d_{i} = 2 \frac{1}{4} |x_{i} - 300| = 370$
$∴ M . D . = \frac{1}{n} Σ |d_{i}| = \frac{1}{7} Σ |x_{i} - 300| = \frac{370}{7} = 52.8$

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