Using the clinic's waiting-time table, what is…

Using the clinic's waiting-time table, what is the median waiting time?

Question 33

HardOriginal question

The table gives a 'less than' cumulative frequency distribution of the waiting times of 40 patients at a clinic.

Waiting time (minutes)	Number of patients
Less than 10	4
Less than 20	11
Less than 30	23
Less than 40	34
Less than 50	40

Using the clinic's waiting-time table, what is the median waiting time?

17.5 minutesCorrect answerYour answer20 minutesCorrect answerYour answer25 minutesCorrect answerYour answer27.5 minutesCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Median class 20–30 (from $n \div 2 = 20$ ). Its frequency is $23 - 11 = 12$ , and cf before it is 11.
Median = $20 + \frac{20 - 11}{12} \times 10$ .
$= 20 + 7.5 = 27.5$ minutes.

Worth noting

17.5 minutes uses 23 as cf, which is the cumulative frequency up to the END of the median class. 25 minutes is the class mark and 20 minutes the lower limit.

Concept: Median of grouped data from a cumulative frequency table
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsFrequency tables

Practise this chapter →

Ten questions from Mean, Median and Mode, at your own pace.

Practise this chapter →

Ten questions from Mean, Median and Mode, at your own pace.

Using the clinic's waiting-time table, what is the median waiting time?

Question 33

Explanation