Statistics, SPM Paper 1 (Short Questions)


Question 5:
A set of data consists of 9, 2, 7, x2 – 1 and 4. Given the mean is 6, find
(a) the positive value of x,
(b) the median using the value of x in part (a).

Solution:
(a)
Mean=6 9+2+7+ x 2 1+4 5 =6                      x 2 +21=30                             x 2 =9                              x=±3 Positive value of x=3.

(b)
Arrange the numbers in ascending order
2, 4, 7, 8, 9
Median = 7


Question 6:
A set of seven numbers has a standard deviation of 3 and another set of three numbers has a standard deviation of 4. Both sets of numbers have an equal mean.
If the two sets of numbers are combined, find the variance.

Solution:
X ¯ 1 = Σ X 1 n 1 m= Σ X 1 7 Σ X 1 =7m m= Σ X 2 3 Σ X 2 =3m σ= Σ X 2 N ( X ¯ ) 2 σ 2 = Σ X 2 N ( X ¯ ) 2 9= Σ X 1 2 7 m 2 63=Σ X 1 2 7 m 2 Σ X 1 2 =7 m 2 +63

Similarly: 16= Σ X 2 2 3 m 2 48=Σ X 2 2 3 m 2 Σ X 2 2 =48+3 m 2 Σ Y 2 =Σ X 1 2 +Σ X 2 2 Σ Y 2 =7 m 2 +63+3 m 2 +48       =10 m 2 +111 ΣY=Σ X 1 +Σ X 2 ΣY=7m+3m=10m Combine Variance: σ 2 = Σ Y 2 N ( ΣY N ) 2 σ 2 = 10 m 2 +111 10 ( 10m 10 ) 2     = 10 m 2 +111 10 m 2     = 10 m 2 +11110 m 2 10     = 111 10 =11.1

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