Question
The heights, h metres, of the 120 boys in an athletics club are recorded.
The table shows information about the heights of the boys.
(a) (i) Write down the modal class.
……………… \(\leq h < ………………\)
(ii) Calculate an estimate of the mean height.
……………………………………… m
(b) (i) One boy is chosen at random from the club.
Find the probability that this boy has a height greater than 1.8m.
………………………………………….
(ii) Three boys are chosen at random from the club.
Calculate the probability that one of the boys has a height greater than 1.8m and the other
two boys each have a height of 1.4m or less.
………………………………………….
(c) (i) Use the frequency table on page 4 to complete the cumulative frequency table.
(ii) On the grid, draw a cumulative frequency diagram to show this information.
(d) Use your diagram to find an estimate for
(i) the median height,
……………………………………… m
(ii) the 40th percentile.
……………………………………… m
Answer/Explanation
(a)(i)To determine the modal class, we need to identify the class interval with the highest frequency that is 1.5 < h ⩽ 1.6
(ii) 1.62 or 1.623…
(b)(i)\(\frac{14}{120}\)
(ii)\(\frac{21}{20060}\)
(c)(i) 55, 79, 106, 120
(ii) Correct diagram
(d)(i) 1.62 to 1.63
(ii) 1.57 to 1.58
Question
(a)
The box-and-whisker plots show the times spent exercising in one week by a group of women and
a group of men.
Below are two statements comparing these times.
For each one, write down whether you agree or disagree, giving a reason for your answer.
(b) The frequency table shows the times, t minutes, each of 100 children spent exercising in one week.
(i) Calculate an estimate of the mean time.
…………………………………… min
(ii) The information in the frequency table is shown in this cumulative frequency diagram.
Use the cumulative frequency diagram to find an estimate of
(a) the 60th percentile,
…………………………………… min
(b) the number of children who spent more than 3 hours exercising.
…………………………………………. [2]
(iii) A histogram is drawn to show the information in the frequency table.
The height of the bar for the interval \(60< t\leq 100\) is 10.8 cm.
Calculate the height of the bar for the interval \(160< t\leq 220.\)
…………………………………….. cm
Answer/Explanation
(a) Disagree: the median for the women is
greater (than the median for the men)
oe
Disagree: the men have a smaller
[interquartile] range of times
(b)(i) 87.4
(ii)(a) 90
(ii)(b) 8
Question
(a) 20 students each record the mass, p grams, of their pencil case.
The table below shows the results.
(i) Calculate an estimate of the mean mass.
g [4]
(ii) Use the frequency table above to complete the cumulative frequency table.[2]
(iii) A student is chosen at random.
Find the probability that this student has a pencil case with a mass greater than 150g.[1]
(b) Some students each record the mass, m kg, of their school bag.
Adil wants to draw a histogram to show this information.
Complete the table below.[2]
(c) The frequency table below shows information about the number of books read by some students in a reading marathon.
(i) The mean number of books read is 4.28 .
Find the value of x.
x = [3]
(ii) Write down the mode.[1]
(iii) Write down the median.[1]
Answer/Explanation
Ans:
7(a)(i) 111.25
7(a)(ii) 2 7 11 17
7(a)(iii) \(\frac{3}{20} oe\)
7(b) 20 6
7(c)(i) 5 nfww
7(c)(ii) 3
7(c)(iii) 4