Short Questions (Question 5 & 6)


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=69+2+7+x21+45=6                    x2+21=30                           x2=9                             x=±3Positive 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:
ˉX1=ΣX1n1m=ΣX17ΣX1=7mm=ΣX23ΣX2=3mσ=ΣX2N(ˉX)2σ2=ΣX2N(ˉX)29=ΣX127m263=ΣX127m2ΣX12=7m2+63

Similarly:16=ΣX223m248=ΣX223m2ΣX22=48+3m2ΣY2=ΣX12+ΣX22ΣY2=7m2+63+3m2+48      =10m2+111ΣY=ΣX1+ΣX2ΣY=7m+3m=10mCombine Variance:σ2=ΣY2N(ΣYN)2σ2=10m2+11110(10m10)2    =10m2+11110m2    =10m2+11110m210    =11110=11.1