17 The table gives information about the heights of 150 students.
Height (\(h\) cm)
Frequency
\(140 \lt h \leqslant 150\)
15
\(150 \lt h \leqslant 155\)
30
\(155 \lt h \leqslant 160\)
51
\(160 \lt h \leqslant 165\)
36
\(165 \lt h \leqslant 180\)
18
(a) On the grid, draw a histogram for this information.(3)
(b) Work out an estimate for the fraction of the students who have a height between 150 cm and 170 cm. (2)
Mark scheme (a)
Working
Answer
Mark
Notes
1.5, 6, 10.2, 7.2, 1.2
Histogram drawn
C1
for 2 correct bars of different widths or at least 3 correct frequency densities.
C1
for all bars in correct proportions or 4 correct bars with axes scaled and labelled.
C1
for fully correct histogram with axes scaled and labelled.
Mark scheme (b)
Answer
Mark
Notes
\(\dfrac{123}{150}\)
M1
for a method to find number of students in interval, eg \(30 + 51 + 36 + \dfrac{1}{3} \times 18\ (= 123)\) or \(150 - 15 - \dfrac{2}{3} \times 18\ (= 123)\)
