Question

A box contains nails of different lengths as shown below, the median class will be:

Length (in cm)	2.0 – 2.5	2.5 – 3.0	3.0 – 3.5	3.5 – 4.0	4.0 – 4.5
No. of nails	5	18	7	11	9

Options

• 2.5 – 3.0

• 3.0 – 3.5

• 3.5 – 4.0

• 4.0 – 4.5

Answer 1

3.0 – 3.5

Explanation:

To determine the median class, we first need to construct a cumulative frequency table:

Length (in cm)	No. of nails (f)	Cumulative Frequency (cf)
2.0 – 2.5	5	5
2.5 – 3.0	18	5 + 18 = 23
3.0 – 3.5	7	23 + 7 = 30
3.5 – 4.0	11	30 + 11 = 41
4.0 – 4.5	9	41 + 9 = 50

1. Find the total frequency (N)

Total number of nails (N) = 5 + 18 + 7 + 11 + 9

= 50

2. Calculate

`N/2 = 50/2`

= 25

3. Identify the median class

Look for the first cumulative frequency that is greater than or equal to 25.

The cumulative frequency for the class interval 2.5 – 3.0 is 23 (which is less than 25).

The cumulative frequency for the next class interval 3.0 – 3.5 is 30 (which is greater than or equal to 25).

Thus, the median value lies within the interval 3.0 – 3.5.