Check your answers if you have time at the end mathsgenie co uk Page 2 1 The cumulative frequency table shows the height, in cm, of some tomato plants
Read each question carefully before you begin answering it Draw a cumulative frequency graph for this information 80 70 60 Cumulative frequency 50
Cumulative frequencies are easy to calculate from a frequency table Cumulative Answer the following questions, giving reasons to support your answers
The times taken by customer service operators to answer 120 telephone calls are illustrated in the cumulative frequency diagram shown below (a) Calculate an
Cumulative Frequency Mark Scheme 1(a) [1] Three correctly summed values [1] All correct values 1(b) (2 ,6) [1] x-co-ordinate -highest value of
On the grid, draw a cumulative frequency graph for your table Answers 7 hours 32 children Approximately 32 children watch TV for less that 7 hours a
Answer ALL the questions Write your answers in the spaces provided in this question paper You must NOT write on the formulae page Anything you write on the
b) Draw a cumulative frequency graph for your table c) Use your graph to find an estimate for (i) the median height of a plant
Starting with the smallest value, give the first two coordinates Pete will plot [2 marks] Answer and Turn over for next question Turn over ? 4
Cumulative Frequency (Inc Interquartile Range) [4 Marks] different method to obtain the correct answer then You should consider to keep using your
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Cumulative Frequency Mark Scheme
1(a) [1] Three correctly summed values [1] All correct values
1(b)ሺʹǡሻ
[1] ݔ-coordinate -highest value of the respective group and coordinate should be the cumulative frequency found in part (a) ሺͶǡͳͻሻ[1] 2
All coordinates plotted correctly[1]
Smooth curve passing through all points[1]
Starting from Ͳ[1]
Turn over Ź
Delay (mins)Frequency Cumulative
Frequency
Ͳ൏ݐʹ
ʹ൏ݐͶͳ͵ͳͻ
Ͷ൏ݐ͵Ͷͷ͵
൏ݐͺͳͻʹ
ͺ൏ݐͳͲͳ͵ͺͷ
ͳͲ൏ݐͳʹͷͻͲ
Time, ܶ
Cumulative
frequency 10 050
ݕ ݔ
100150200250300
0 20 30
40
50
60
70
80
90
3(a)͉͵ͶͲേͷ[1] line drawn across and down
from CF ൌͷͲ
3(b)͉ʹͲേͷ[1] line drawn across and down
from CF ൌʹͷ
3(c)͉ͶͲͲേͷ[1] line drawn across and down
from CF ൌͷ
3(d)͉ͳͶͲേͳͲ[1] Value found in part (c) (b)
3(e)Draw up from ͉ͷͲͲ. Intersect graph at ͻͶ[1]
people spent over ͉ͷͲͲ[1]
4(a)[1] Cumulative frequency values
calculated [1] Cumulative frequency plotted against Upper bound of group [1] Smooth curve
Turn over Ź
Time taken
()Frequency CF
Ͳ൏ݐʹͲʹʹ
ʹͲ൏ݐ͵ͲͳʹͳͶ
͵Ͳ൏ݐͶͲʹ͵͵
4Ͳ൏ݐͷͲ͵Ͳ
ͷͲ൏ݐͲͳͶͺͳ
Ͳ൏ݐͲͷͺ
Ͳ൏ݐͻͲͶͻͲ
Time taken, ܶ
Cumulative Frequency
10 010 ݕ ݔ
2030405060
0 20 30
40
50
60
70
80
90
100
708090
4(b)
Lower quartile ൌ͵Ͷേʹ
Upper quartile ൌͷͲേʹ[1]
Inter quartile range= ͳേͶ[1]
4(c) Line drawn up from Ͷͷminutes, intersecting curve. (Shown above)[1]
Ͷ͵േʹ[1]
Turn over Ź
Time taken, ܶ
Cumulative Frequency
10 010 ݕ ݔ
2030405060
0 20 30
40
50
60
70
80
90
100
708090
Time taken, ܶ
Cumulative Frequency
10 010 ݕ ݔ
2030405060
0 20 30
40
50
60
70
80
90
100
708090
5(a)ͺ͵െ͵ͳ[1]
ͷʹሺേʹሻ[1]
5(b)[1] Median compared
[1] IQR compared
6(a)Graham has used straight lines to join the points
rather then a smooth curve. [1] Graham plotted the data at the start of each interval instead of the mid-point.[1] Graham only plotted the cumulative frequency up to
94 instead of 100. [1]
6(b)
Upper of the group plotted against cumulative
frequency [1] All points plotted correctly.
Smooth curve through all points. [1]
END
Age in Years
Cumulative
Frequency
10 010 ݕ
ݔ20304050600
20 30
40
50
60
70
80
90
100
708090
Amount spent (£)
Cumulative
Frequency
10 010 ݕ
ݔ20304050600
20 30
40
50
60
70
80
90
100