13 Charlotte grows some potatoes. The table shows information about the weights of her potatoes.
Weight (\(w\) grams)
Frequency
\(100 \lt w \leqslant 120\)
5
\(120 \lt w \leqslant 140\)
25
\(140 \lt w \leqslant 160\)
30
\(160 \lt w \leqslant 180\)
15
\(180 \lt w \leqslant 200\)
5
(a) Complete the cumulative frequency table.
Weight (\(w\) grams)
Cumulative frequency
\(100 \lt w \leqslant 120\)
\(100 \lt w \leqslant 140\)
\(100 \lt w \leqslant 160\)
\(100 \lt w \leqslant 180\)
\(100 \lt w \leqslant 200\)
(1)
(b) On the grid opposite, draw a cumulative frequency graph for your table.(2)
(c) Use your graph to find an estimate for the interquartile range. (2)
(d) Use your graph to find an estimate for the percentage of Charlotte’s potatoes with a weight less than 150 grams. (3)
Mark scheme (a)
Answer
Mark
Notes
5, 30, 60, 75, 80
1
B1 for correct cumulative frequencies (may be implied by correct heights on the grid)
Mark scheme (b)
Answer
Mark
Notes
cf graph
2
M1 for at least 4 of the 5 points plotted correctly at the ends of the intervals or 4 of the 5 points plotted not at the ends but consistently within each interval and joined (dep on a cf table with no more than one arithmetic error) A1 for a fully correct cf graph (points may be joined by a curve or straight line segments)
Mark scheme (c)
Working
Answer
Mark
Notes
IQR = UQ – LQ
26-28
2
M1 for reading values from their cf graph at cf = 20 or 20.25 and cf = 60 or 60.75 A1ft provided M1 is awarded in (b)
Mark scheme (d)
Answer
Mark
Notes
55-59
3
M1 for reading a value from their cf graph at weight 150 grams M1 for \(\dfrac{\text{``}45\text{''}}{\text{``}80\text{''}} \times 100\) A1ft provided M1 is awarded in (b)
