The table below presents the cumulative frequency distribution of delay times (in minutes) for 50 regional flights recorded at an airport: | Delay Time (minutes) | Cumulative Frequency | | :--- | :--- | | 10 - 19 | 8 | | 20 - 29 | 20 | | 30 - 39 | 40 | | 40 - 49 | 50 | What is the 70\text{th} percen

The table below presents the cumulative frequency distribution of delay times (in minutes)… — JAMB UTME

The table below presents the cumulative frequency distribution of delay times (in minutes) for $50$ regional flights recorded at an airport:

What is the $70\text{th}$ percentile of the delay times?

The

70\text{th}

percentile of the delay times is

37.0

minutes.

The

70\text{th}

percentile position is found by taking

70\%

50

, which yields

35

. Looking at the cumulative frequency table, the 35th item falls in the

30 - 39

interval (class boundaries

29.5 - 39.5

). Applying the percentile interpolation formula:

P_{70} = 29.5 + \left(\frac{35 - 20}{20}\right) \times 10 = 29.5 + 7.5 = 37.0\text{ minutes}

Determine the position of the 70th percentile rank.

Position rank

= \frac{70}{100} \times 50 = 35\text{th value}

The 70th percentile corresponds to 70% of the total frequency

N = 50

Identify the 70th percentile class interval and its parameters.

Interval:

30 - 39

; Lower class boundary

L = 29.5

, cumulative frequency preceding class

F = 20

, frequency of percentile class

f = 20

, class width

c = 10

The cumulative frequency reaches 20 at

29.5

and 40 at

39.5

, so the 35th value lies in the

30 - 39

class interval.

Apply the percentile interpolation formula

P_{70} = L + \left(\frac{\frac{70N}{100} - F}{f}\right) \times c

P_{70} = 29.5 + \left(\frac{35 - 20}{20}\right) \times 10 = 29.5 + \left(\frac{15}{20}\right) \times 10 = 29.5 + 7.5 = 37.0\text{ minutes}

Linear interpolation distributes the cumulative frequencies evenly across the class interval.

Calculating percentiles from grouped cumulative frequency data using class boundaries and linear interpolation.