The table below shows the distribution of scores achieved by 50 candidates on a professional certification assessment: | Score | Number of Candidates | |---|---| | 60 | 4 | | 70 | 11 | | 80 | 20 | | 90 | 10 | | 100 | 5 | What is the interquartile range (IQR) of the assessment scores?

The table below shows the distribution of scores achieved by 50 candidates on a profession… — GMAT

The table below shows the distribution of scores achieved by $50$ candidates on a professional certification assessment:

Score	Number of Candidates
$60$	$4$
$70$	$11$
$80$	$20$
$90$	$10$
$100$	$5$

What is the interquartile range (IQR) of the assessment scores?

A
$10$
$20$ Answer
C
$30$
D
$35$
E
$40$

Answer

The interquartile range of the assessment scores is

20

To find the interquartile range (IQR), first find

Q_1

(

25\text{th}

percentile) and

Q_3

(

75\text{th}

percentile). With

50

total candidates,

Q_1

is situated around position

12.5

, which falls into the score of

70

Q_3

is situated around position

37.5

, which falls into the score of

90

. Subtracting

Q_1

from

Q_3

yields

90 - 70 = 20

Step-by-Step Solution

Calculate the cumulative frequency distribution to find score positions.

Score

60

: candidates

1

4

; Score

70

: candidates

5

15

; Score

80

: candidates

16

35

; Score

90

: candidates

36

45

; Score

100

: candidates

46

50

. Total

N = 50

Cumulative frequencies identify the precise position of ranked scores.

Determine the first quartile (

Q_1

), which represents the

25\text{th}

percentile.

The

25\text{th}

percentile corresponds to the

0.25 \times 50 = 12.5\text{th}

position. Looking at the cumulative frequencies, candidate positions

5

through

15

all scored

70

, so

Q_1 = 70

The first quartile marks the score boundary below which

25\%

of the dataset falls.

Determine the third quartile (

Q_3

), which represents the

75\text{th}

percentile.

The

75\text{th}

percentile corresponds to the

0.75 \times 50 = 37.5\text{th}

position. Candidate positions

36

through

45

all scored

90

, so

Q_3 = 90

The third quartile marks the score boundary below which

75\%

of the dataset falls.

Compute the interquartile range

(\text{IQR} = Q_3 - Q_1)

\text{IQR} = 90 - 70 = 20.

The interquartile range measures the spread of the middle

50\%

of the distribution.

Key Concept

Interquartile Range (IQR) and Quartile Positions in Frequency Distributions

Question

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