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+x2−1+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
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+x2−1+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=ΣX127−m263=ΣX12−7m2ΣX12=7m2+63
Similarly:16=ΣX223−m248=ΣX22−3m2ΣX22=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+11110−m2 =10m2+111−10m210 =11110=11.1
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=ΣX127−m263=ΣX12−7m2ΣX12=7m2+63
Similarly:16=ΣX223−m248=ΣX22−3m2ΣX22=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+11110−m2 =10m2+111−10m210 =11110=11.1