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 following table presents the cumulative frequencies for each class interval.

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

The cumulative frequency immediately greater than \( \frac{n}{2} \) (which is \( \frac{30}{2} = 15 \)) is 19, corresponding to the class interval 55-60.

The median class is 55-60.

The lower limit (\(l\)) of the median class is 55.

The frequency (\(f\)) of the median class is 6.

The cumulative frequency (\(cf\)) of the median class is 13.

The class size (\(h\)) is 5.

The formula for the median is \( l + (\frac{\frac{n}{2} - cf}{f} \times h)\).

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

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

Median = 56.67

Therefore, the median weight is 56.67 kg.