1
Statistics
Paper1
1.
At a conference of 100 mathematicians there are 72 men and 28 women. The men have a mean
height of 1.79 m and the women have a mean height of 1.62 m. Find the mean height of the 100
mathematicians.
2.
The mean of the population
x
1
,
x
2
,
........
,
x
25
is
m
. Given that
25
1
i
i
x
= 300 and
25
1
2
)
–
(
i
i
m
x
= 625, find
(a)
the value of
m
;
(b)
the standard deviation of the population.
3.
The cumulative frequency curve below shows the marks obtained in an examination by a group
of 200 students.
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
10
20
30
40
50
60
70
80
90
100
Mark obtained
Number
of
students
(a)
Use the cumulative frequency curve to complete the frequency table below.
Mark (
x
)
0
x
< 20
20
x
< 40
40
x
< 60
60
x
< 80
80
x
< 100
Number of
students
22
20
(b)
Forty percent of the students fail. Find the pass mark.
4.The cumulative frequency curve below shows the heights of 120 basketball players in centimetres.

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120
110
100
90
80
70
60
50
40
30
20
10
0
160
165
170
175
180
185
190
195
200
Height in centimetres
Number of players
Use the curve to estimate
(a) the median height; (b) the interquartile range.
5.The four populations A, B, C and D are the same size and have the same range. Frequency histograms for the four populations are given below.
......
......
......

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6.
The cumulative frequency graph below shows the heights of 120 girls in a school.
130
120
110
100
90
80
70
60
50
40
30
20
10
0
185
180
175
170
165
160
155
150
Cumulative frequency
Height in centimetres
(a)
Using the graph
(i)
write down the median;
(ii)
find the interquartile range.
(b)
Given that 60
of the girls are taller than
a
cm, find the value of
a
.
7.
A test marked out of 100 is written by 800 students. The cumulative frequency graph for the
marks is given below.

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