Question
a) The box-and-whisker plot shows information about the marks scored by some students in a test.
(i) Write down the median mark. ………………………………………….
(ii) Work out the range.
………………………………………….
(iii) Jais scored a mark in the test that was higher than the marks scored by 75% of the students.
Write down a possible mark for Jais. ………………………………………….
(iv) This box-and-whisker plot shows information about the marks scored by the same students in
a second test.
Make one comparison between the distributions of marks in the two tests.
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
(b) The table shows information about the height, h cm, of each of 50 plants.
Calculate an estimate of the mean.
…………………………………….. cm
(c) Some apples are weighed and the mass, m grams, of each apple is recorded.
The table shows the results.
The histogram shows some of the information from the table.
(i) Work out the value of x.
x = …………………………………………
(ii) Complete the histogram.
Answer/Explanation
(a)(i) 70
(ii) 78
(iii) Value in range 86 <V ≤ 90
(iv) One general comment interpreting
the median comparison nfww
e.g. Students did better on second test
oe
OR
One general comment interpreting
IQR/range comparison nfww
e.g. Students marks were more
consistent on the 2nd test oe
(b) 31.2
(c)(i) 38
(ii) Blocks of heights 4.4 and 3.4 with
correct widths
Question
The table shows information about the mass, m grams, of each of 120 letters.
(a) Calculate an estimate of the mean mass. …………………………………….g
(b) Iraj draws a histogram to show this information.
He makes the height of the first bar 17.2cm.
Calculate the height of each of the remaining bars.
(c) Complete the cumulative frequency table.
(d) Draw a cumulative frequency diagram.
(e) Use the cumulative frequency diagram to find an estimate for
(i) the median,
(ii) the upper quartile,
(iii) the 40th percentile,
(iv) the number of letters with a mass m where
Answer/Explanation
5(a) 121 or 120.8… or 120 \(\frac{5}{6}\)
5(b) 12.4 5 1.4
5(c) 43 74 99 120
5(d) Correct diagram
5(e)(i) Strict FT their median reading 1
5(e)(ii) Strict FT their UQ reading 1
5(e)(iii) Strict FT their reading at\( 40^{th}\)percentile
5(e)(iv) Strict FT their reading at 400
– their reading at 250
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