The table below shows the distribution of monthly fuel consumption (in liters) for a sampl… — JAMB UTME

The table below shows the distribution of monthly fuel consumption (in liters) for a sample of $50$ commercial transport vehicles operated by a logistics firm in Lagos:

Fuel Consumption (Liters)	Frequency ( $f$ )
10 – 19	8
20 – 29	13
30 – 39	16
40 – 49	9
50 – 59	4

Calculate the median fuel consumption (in liters) for this sample of vehicles.

Answer: 32 liters

Answer

The median fuel consumption for the sample of vehicles is

32

liters.

The median of a grouped frequency distribution is computed using continuous class boundaries. With

N=50

, the median position is

25

. The

30–39

class has lower boundary

29.5

, frequency

16

, preceding cumulative frequency

21

, and class interval

10

. Substituting these values gives

29.5 + \frac{25 - 21}{16} \times 10 = 32

liters.

Step-by-Step Solution

Calculate the total frequency (

N

) and construct cumulative frequencies (

cf

Total frequency

N = 8 + 13 + 16 + 9 + 4 = 50

. Cumulative frequencies are: 10–19 (

cf = 8

), 20–29 (

cf = 21

), 30–39 (

cf = 37

), 40–49 (

cf = 46

), 50–59 (

cf = 50

Cumulative frequencies are required to identify the class containing the median value.

Locate the median position and determine the median class parameters.

Position

= \frac{N}{2} = \frac{50}{2} = 25

. The

25^{\text{th}}

item falls in the

30 - 39

class. Lower boundary (

L

)

= 29.5

, preceding cumulative frequency (

cf_p

)

= 21

, median class frequency (

f_m

)

= 16

, class width (

c

)

= 10

The median class is the first class whose cumulative frequency meets or exceeds

N/2

Substitute the parameters into the grouped median formula.

\text{Median} = L + \left(\frac{\frac{N}{2} - cf_p}{f_m}\right) \times c = 29.5 + \left(\frac{25 - 21}{16}\right) \times 10 = 29.5 + \left(\frac{4}{16}\right) \times 10 = 29.5 + 2.5 = 32

Linear interpolation within the median class yields the precise median measurement.

Key Concept

Median of Grouped Data using Class Boundaries and Linear Interpolation

Estimated Time:2m 0s

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