Question

Consider a data set containing the following values: 67, 94, 82, 80, 97, 99, 78, 91. The mean of the given value is 86. The squares of the scores are calculated as follows: 4,489, 8,836, 6,724, 6,400, 9,409, 9,801, 6,084, 8,281. If the preceding scores are sample data, the sum of squares are? If the preceding scores are population data, the SS is? If preceding scores in a sample data, the simple standard deviation is? and the sample variance is? If the preceding scors are population data, the population standard deviation is? and the population variance is?

Answer 1

S.No	X1		X12
1	67.00		4489.0000
2	94.00		8836.0000
3	82.00		6724.0000
4	80.00		6400.0000
5	97.00		9409.0000
6	99.00		9801.0000
7	78.00		6084.0000
8	91.00		8281.0000
ΣX	688	ΣX2	60024.0000

1)If the preceding scores are sample data, the sum of squares are = $\sum$ x²-( $\sum$ x)²/n=60024-688²/8

=856

2) If the preceding scores are population data, the SS is $\sum$ x²-( $\sum$ x)²/n= 856

3)

If preceding scores in a sample data, the simple standard deviation is =(SS/(n-1))^1/2 =11.058

4) sample variance =SS/(n-1) =122.2857

5) If the preceding scors are population data, the population standard deviation=(SS/(n)^1/2 =10.344

6) population variance is =SS/n =107