Sets---Mean, Median

Question

1. Use the data set {5, 21, 21, 25, 30, 40} to find the requested values:

a. Mean

b. Median

c. Mode

d. Range

e. Standard deviation

Answer 1

The data set has n=6 observations.

 

Mean: (5 + 21 + 21 + 25 + 30 + 40)/6 = 71/3 = 23.666...

 

Median: (21 + 25)/2 = 23

 

Mode: 21 (Happens twice)

 

Range: 5 ≤ x ≤ 40

 

Standard deviation:

 

s = √[∑(x_i - x_m)²/(n-1)]

 

= √[((5 - 71/3)² + (21 - 71/3)² + (21 - 71/3)² + (25 - 71/3)² + (30 - 71/3)² + (40 - 71/3)²)/5]

 

= √[(3136/9 + 64/9 + 64/9 + 16/9 + 361/9 + 2401/9)/5]

 

= √(6042/45)

 

= √(2014/15)

 

= 11.587...