Question

Consider the following sample data:

30	32	22	49	28	32

a. Calculate the range.

b. Calculate MAD. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c. Calculate the sample variance. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

d. Calculate the sample standard deviation. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Answer 1

Solution:

Given that,

Arrange the lowest to highest

22, 28, 30, 32, 32, 49

n = 6

a) The range = 49 - 22 = 27

b )The mean of sample is   

x/n =  (22 + 28 + 30 + 32 + 32 + 49 / 6)

   = 193 / 6

= 32.1667

= ( 22 - 32.1667 ) + ( 28 - 32.1667) + (30 - 32.1667) + (32 - 32.1667) + ( 32 - 32.1667) + (49 - 32.1667) / 6

= 10.1667 + 4.1667 + 2.1667 + 0.1667 + 0.1667 + 16.8333 / 6

= 33.6668 / 6

MAD = 5.61

c) Sample variance is s²

s² = 1/(n-1)(x - )²

⁼  1/6 - 1 (22 - 32.1667)²+ (28 - 32.1667 )²+ (30 - 32.1667)²+ (32 - 32.1667)² +( 32 - 32.1667 )² + ( 49 - 32.1667 )²

= 1/5 (103.3618 + 17.3614 + 4.6946 + 0.0278 + 0.0278 + 283.3600)

= 408.8334 / 5

= sample variance = s² = 81.77

d) sample standard deviation = s = 81.77

The sample standard deviation is = s = 9.04