# CBSE Class 10 Math Question Paper 2018 | Q22

###### CBSE Math Board Paper 2018 Solution | 3 Mark | Statistics - Median

This statistics question is a three mark question that appeared in CBSE class 10 Math board paper in 2018. A relatively easy question.

Question 22: The table below shows the salaries of 280 persons. Calculate the median salary of the data.

Salary (In thousands) No. of Persons
5 - 10 49
10 - 15 133
15 - 20 63
20 - 25 15
25 - 30 6
30 - 35 7
35 - 40 4
40 - 45 2
45 - 50 1

## NCERT Solution to Class 10 Maths

### Explanatory Answer | CBSE Class 10 2018 Board Paper Q22

#### Step 1: Compute Cumulative Frequency

Salary (In thousands) No. of Persons Cumulative Frequency
5 - 10 49 49
10 - 15 133 182
15 - 20 63 245
20 - 25 15 260
25 - 30 6 266
30 - 35 7 273
35 - 40 4 277
40 - 45 2 279
45 - 50 1 280

#### Step 2: Compute the Median Class

The number of employees, n = 280
∴ $$frac{n}{2}$ = 140 140 falls under the 10 - 15 class ∴ The median class is 10 - 15 #### Step 3: Compute Median Value of median = l + $\frac{$n/2$ - cf}{f}) × h
l = lower limit of median class = 10
$\frac{n}{2}$ = 140
cf - cumulative frequency of class before the median class = 49
f - frequency of median class = 133
h - class size = 5

Median = 10 + $\frac{140 - 49}{133}$ × 5 = 10 + $\frac{91}{133}$ × 5
Median = 10 + $\frac{13}{19}$ × 5 = 10 + $\frac{65}{19}$
Median = 10 + 3.42 = 13.42

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