Using the homework-time table, what is the…

Using the homework-time table, what is the median time spent on homework?

Question 28

MediumOriginal question

A school recorded how long 50 students spent on homework one evening.

Time (minutes)	Number of students
0–20	7
20–40	11
40–60	16
60–80	10
80–100	6

Using the homework-time table, what is the median time spent on homework?

28.75 minutesCorrect answerYour answer40 minutesCorrect answerYour answer44.375 minutesCorrect answerYour answer48.75 minutesCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Median class 40–60: $l = 40$ , $cf = 18$ , $f = 16$ , $h = 20$ , $\frac{n}{2} = 25$ .
Median = $l + \frac{\frac{n}{2} - cf}{f} \times h = 40 + \frac{25 - 18}{16} \times 20$ .
$= 40 + \frac{140}{16} = 40 + 8.75 = 48.75$ minutes.

Worth noting

28.75 minutes uses 34, the cumulative frequency up to and including the median class, as cf. 44.375 minutes uses $h = 10$ instead of the class width 20, and 40 minutes is only the lower limit.

Concept: Median of grouped data by formula
Typical timeTypical: 70 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 homework-time table, what is the median time spent on homework?

Question 28

Explanation