The table below presents the distribution of daily expenditure on diesel (in ₦\text{'000}) by 40 micro-enterprises in a commercial hub: | Daily Expenditure (₦\text{'000}) | Number of Enterprises (f) | |---|---| | 10 - 19 | 6 | | 20 - 29 | 10 | | 30 - 39 | 14 | | 40 - 49 | 7 | | 50 - 59 | 3 | What is

The table below presents the distribution of daily expenditure on diesel (in ₦\text{'000})… — JAMB UTME

The table below presents the distribution of daily expenditure on diesel (in $₦\text{'000}$ ) by $40$ micro-enterprises in a commercial hub:

What is the median daily expenditure on diesel for these enterprises?

The median daily expenditure on diesel is

₦32.36\text{ thousand}

The median of grouped data is computed using the formula

\text{Median} = L + \left(\frac{\frac{N}{2} - F}{f}\right) c

. For this distribution, total frequency

N = 40

, giving a median position of

20

. Cumulative frequency reveals that the median class is

30 - 39

. The lower boundary

L

29.5

, the cumulative frequency of preceding classes

F

16

, the frequency of the median class

f

14

, and the class width

c

10

. Substituting these values gives

29.5 + \left(\frac{20 - 16}{14}\right) \times 10 = 32.36\text{ thousand Naira}

Determine total frequency and find the median position

Total frequency

N = 6 + 10 + 14 + 7 + 3 = 40

. Median position

= \frac{N}{2} = \frac{40}{2} = 20^{\text{th}}

item.

The median in grouped data corresponds to the value at the half-way position of total observations.

Calculate cumulative frequencies to identify the median class

Cumulative frequencies are

6, 16, 30, 37, 40

. The

20^{\text{th}}

observation lies within the class

30 - 39

The cumulative frequency reaches

30

in the

30 - 39

group, which exceeds

20

Identify class parameters for the median formula

Lower class boundary

L = 29.5

, preceding cumulative frequency

F = 16

, class frequency

f = 14

, class interval width

c = 39.5 - 29.5 = 10

Accurate calculation requires continuous boundaries rather than discrete limits.

Apply the grouped median formula

\text{Median} = L + \left(\frac{\frac{N}{2} - F}{f}\right) \times c = 29.5 + \left(\frac{20 - 16}{14}\right) \times 10 = 29.5 + \left(\frac{4}{14}\right) \times 10 = 29.5 + 2.857 = 32.357 \approx 32.36

Evaluates the linear interpolation within the median class interval.

Calculating median for grouped statistical frequency distributions using class boundaries.