# For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is -

Latika Leekha
8 years ago
The size of each data set is 5 i.e. N = 5.
Let M1 and M2 denote the means of the two data sets.
Let V1 and V2 be the variance.
Then, we have V1 = 4 which means 1/5 Σ xi2 – 22 = 4
Hence, 1/5 Σ xi2 = 16 which gives Σ xi2 = 40.
Also, we have V2 = 5 which means 1/5 Σ yi2 – 42 = 5
Hence, 1/5 Σ yi2 = 21 which gives Σ yi2 = 105.
Hence, we have Σ ( xi2 + yi2 ) = 145
Also Σ xi = N .M1 = 5. 2 = 10
Similarly, Σ yi = N .M2 = 5. 4 = 20
So, Σ (xi + yi) = 10+20 = 30.
Variance of the combined data set = 1/10 Σ ( xi2 + yi2 ) – (1/10 Σ (xi + yi) )2
= 145/10 – 9
= 55/10
= 11/2.
Thanks & Regards
Latika Leekha