The bar chart shows the number of books read by 25 students during the summer holidays. 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Number of books Frequency © EAGLE BEAC...
Question 1 Report
The bar chart shows the number of books read by 25 students during the summer holidays.
- Write down the total number of students who took part in the survey. (1)
- Find the modal number of books read. (1)
- Find the median number of books read. (1)
- Calculate the mean number of books read. (2)
Answer Details
Reading frequencies from a bar chart makes it possible to find the mode (the tallest bar), the median (the middle value once the data is placed in order) and the mean (the total divided by the number of students), just as with a frequency table.
(a) Adding every bar's frequency: \(3 + 5 + 8 + 6 + 2 + 1 = 25\) students took part in the survey. [1 mark]
(b) The tallest bar, with frequency 8, is at 2 books, so the mode is 2 books. [1 mark]
(c) With 25 students, the median is the 13th value once ordered. The cumulative frequencies are 3, 8, 16, 22, 24, 25; the 13th value falls in the "2 books" group, since the cumulative total passes 8 (end of "1 book") and reaches 16 within "2 books," so the median is 2 books. [1 mark]
(d) The total number of books read is \(0(3) + 1(5) + 2(8) + 3(6) + 4(2) + 5(1) = 0 + 5 + 16 + 18 + 8 + 5 = 52\); dividing by 25 gives a mean of \(52 \div 25 = 2.08\) books. [2 marks]
Here the mode and median agree (both 2 books), but the mean (2.08) is slightly higher, pulled up by the smaller number of students who read 3, 4 or 5 books; all three measures are valid summaries, but they answer slightly different questions about the data.
Download The App On Google Playstore
Everything you need to excel in your exams
