The table below presents the cumulative frequency distribution of examination marks for 60 candidates: | Mark Boundary | Cumulative Frequency | | :---: | :---: | | < 20.5 | 5 | | < 40.5 | 18 | | < 60.5 | 42 | | < 80.5 | 54 | | < 100.5 | 60 | How many candidates scored between 40.5 and 80.5 marks?

The table below presents the cumulative frequency distribution of examination marks for 60… — JAMB UTME

The table below presents the cumulative frequency distribution of examination marks for $60$ candidates:

How many candidates scored between $40.5$ and $80.5$ marks?

Answer: 36 candidates

36 candidates

To find the number of candidates with scores between

40.5

and

80.5

, subtract the cumulative frequency of scores below

40.5

(

18

) from the cumulative frequency of scores below

80.5

(

54

). This gives

54 - 18 = 36

Find the cumulative frequency up to the upper boundary of

80.5

Cumulative frequency (

F_{\text{upper}}

) =

54

This represents the total number of candidates scoring below

80.5

marks.

Find the cumulative frequency up to the lower boundary of

40.5

Cumulative frequency (

F_{\text{lower}}

) =

18

This represents the total number of candidates scoring below

40.5

marks.

Calculate the number of candidates within the interval

(40.5, 80.5)

by finding the difference

54 - 18 = 36

Subtracting the cumulative frequency at

40.5

from that at

80.5

isolates the count of candidates within this specific mark range.

Finding class frequency from cumulative frequency boundaries