Answer:
(a) 2.3
(b) 0.5245
(c) 0.7242
(d) 0.5245
Step-by-step explanation:
The data provided is:
S = {180.5, 181.7, 180.9, 181.6, 182.6, 181.6, 181.3, 182.1, 182.1, 180.3, 181.7, 180.5}
(a)
The formula to compute the sample range is:
The data set arranged in ascending order is:
S' = {180.3
, 180.5
, 180.5
, 180.9
, 181.3
, 181.6
, 181.6
, 181.7
, 181.7
,, 182.1
, 182.1
, 182.6}
The minimum value is, 180.3 and the maximum value is, 182.6.
Compute the sample range as follows:
Thus, the sample range is 2.3.
(b)
Compute the sample variance as follows:
Thus, the sample variance is 0.5245.
(c)
Compute the sample standard deviation as follows:
Thus, the sample standard deviation is 0.7242.
(d)
Compute the sample variance using the shortcut method as follows:
Thus, the sample variance is 0.5245.