Question

Consider the following data:

14,4,6,10,3,5

Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place.

Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place.

Step 3 of 3: Calculate the value of the range.

Answer 1

Solution:

Step 1 of 3:

$\bar{x}$ = $\sum$ (X) / n

= ( 14+4+6+10+3+5) / 6

= 72/6

= 7

Sample Variance :

= $\sum$ ( X - $\bar{x}$ )² / n - 1

= ( 14 - 7 )² + ( 4 - 7 )² + ( 6 - 7 )²​​​​​​​ + ( 10 - 7 )²​​​​​​​ + ( 3 - 7 )²​​​​​​​ + ( 5 - 7 )²​​​​​​​ / 6 - 1

= 88 / 5

= 17.6

Step 2 of 3:

Sample standard deviation:

s = $\sqrt{}$ $\sum$ ( X - $\bar{x}$ )² / n - 1

= $\sqrt{}$ Sample variance

= $\sqrt{}$ 17.6

= 4.2

Step 3 of 3:

Range:

Range = Max - min

= 14 - 3

= 11