# Compute Mean Deviation from Mean of the Following Distribution: Mark 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of Students 8 10 15 25 20 18 9 5 - Mathematics

Compute mean deviation from mean of the following distribution:

 Mark 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of students 8 10 15 25 20 18 9 5

#### Solution

Computation of mean deviation from the mean:

 Marks Number of Students $f_i$ Midpoints $x_i$ $f_i x_i$ $\left| x_i - X \right|$ = $\left| x_i - 49 \right|$ $f_i \left| x_i - X \right|$ 10−20 8 15 120 34 272 20−30 10 25 250 24 240 30−40 15 35 525 14 210 40−50 25 45 1125 4 100 50−60 20 55 1100 6 120 60−70 18 65 1170 16 288 70−80 9 75 675 26 234 80−90 5 85 425 36 180 $N = \sum^8_{i = 1} f_i = 110$ $\sum^8_{i = 1} f_i x_i = 5390$ $\sum^8_{i = 1} f_i \left| x_i - X \right| = 1644$
$N = \sum^8_{i = 1} f_i = 110$
and

$\sum^8_{i = 1} f_i x_i = 5390$

$X = \frac{\sum^8_{i = 1} f_i x_i}{N}$
$= \frac{5390}{110}$
$= 49$

$\text{ Mean deviation } = \frac{\sum^8_{i = 1} f_i \left| x_i - X \right|}{N}$

$= \frac{1644}{110}$

$= 14 . 945$

$\approx 14 . 95$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.3 | Q 3 | Page 16