EXERCISES IN STATISTICS
Series A, No. 1
1. The number of children recorded to each of 25 families were
2
,
4
,
1
,
0
,
1
,
3
,
0
,
4
,
2
,
6
,
0
,
0
,
2
,
3
,
1
,
5
,
4
,
0
,
3
,
1
,
2
,
5
,
3
,
4
,
1
.
(a) Construct a frequency table and a graph for the distribution of family
size in this sample.
(b) Find the sample mean and the standard deviation.
Answer:
x
i
f
i
f
i
x
i
x
2
i
f
i
x
2
i
0
IIIII
5
0
0
0
1
5
5
1
5
2I
I
I
I
4
8
4
1
6
3
IIII
4
12
9
36
4
4
16
16
64
5
II
2
10
25
50
6
I
1
6
36
36
25
57
207
∑
f
i
∑
f
i
x
i
∑
f
i
x
2
i
We ±nd that
Mean =
∑
f
i
x
i
∑
f
i
=
∑
fix
i
N
=
57
25
=2
.
28
We can say that the average number of children per family is 2.28. One should
take care to state this correctly. For example, it is absurd to say that “The
average family has 2.28 children”. We also ±nd that
Variance =
∑
f
i
(
x
i
−
¯
x
)
2
N
=
∑
f
i
x
2
i
N
−
µ ∑
f
i
x
i
N
¶
2
=
207
25
−
µ
57
25
¶
2
=3
.
082
1