The table below presents the frequency distribution of monthly sales revenue (in ₦\text{'0… — JAMB UTME

The table below presents the frequency distribution of monthly sales revenue (in $₦\text{'000}$ ) recorded by a sample of $50$ retail traders in a urban commercial center:

Sales Revenue ( $₦\text{'000}$ )	Number of Traders ( $f$ )
10 �� 19	8
20 – 29	12
30 – 39	16
40 – 49	10
50 – 59	4

Calculate the estimated median sales revenue (in $₦\text{'000}$ ) for the traders.

Cevap: 32.63 ₦'000

Cevap

The estimated median sales revenue is 32.63 thousand Naira (

₦32,625

To calculate the median of grouped data, determine the total frequency (

N = 50

) and the median position (

\frac{N}{2} = 25

). The cumulative frequency distribution shows that the

25\text{th}

observation falls within the

30\text{ – }39

interval. Using the lower class boundary

L = 29.5

, cumulative frequency of prior classes

F = 20

, median class frequency

f = 16

, and class length

c = 10

, the formula

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

yields

29.5 + \left(\frac{25 - 20}{16}\right) \times 10 = 32.625

, which equals

32.63

when rounded to two decimal places.

Adım Adım Çözüm

Calculate the total frequency and median position

Total frequency

N = 50

, median rank =

\frac{N}{2} = 25

The median of a frequency distribution is located at the middle position

\frac{N}{2}

Determine cumulative frequencies and identify the median class

Cumulative frequencies are

8

20

36

46

, and

50

. The median class is 30 – 39

Since

20

items fall below

30

, the

25\text{th}

item lies within the

30\text{ – }39

class interval.

Extract interpolation parameters for the median class

Lower class boundary

L = 29.5

, preceding cumulative frequency

F = 20

, class frequency

f = 16

, class interval width

c = 10

The continuous class boundary between

29

and

30

29.5

, and interval width is

19.5 - 9.5 = 10

Compute the linear interpolation for grouped median

\text{Median} = 29.5 + \left(\frac{25 - 20}{16}\right) \times 10 = 29.5 + 3.125 = 32.625 \approx 32.63

Applying the standard grouped data median formula yields the precise interpolated value.

Anahtar Kavram

Grouped Data Median Calculation

Soru

Cevap

Adım Adım Çözüm

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