Question

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg)	40 - 45	45 - 50	50 - 55	65 - 60	70- 65	65 - 70	70 - 75
Number of students	2	3	8	6	6	3	2

Answer 1

The cumulative frequencies with their respective class intervals are as follows.

Weight (in kg)	Frequency (f\(_i\))	Cumulative frequency
40 - 45	2	2
45 - 50	3	2 + 3 = 5
50 - 55	8	5 + 8 = 13
65 - 60	6	13 + 6 = 19
70- 65	6	19 + 6 = 15
65 - 70	3	25 + 3 = 28
70 - 75	2	28 + 2 = 30
Total (n)	30

Cumulative frequency just greater \(\frac{n}2 ( i.e., \frac{30}2 = 15)\) than is 19, belonging to class interval 55−60.
Median class = 55−60
Lower limit (\(l\)) of median class = 55
Frequency (\(f\)) of median class = 6
Cumulative frequency (\(cf\)) of median class = 13
Class size (\(h\)) = 5

 Median = \( l + (\frac{\frac{n}2 - cf}f \times h)\)

Median =  \(55 + (\frac{15 - 13}6 \times 5)\)

Median = 55 + \( \frac{10}6\)
Median = 56.67

Therefore, median weight is 56.67 kg.