Question

Calculate the requested statistics for the following sample data:

     11,     13,     5,     13,     7,     8

Give the answer to the proper number of decimal places outlined below •.
.

(a) mean =

(b) median =

(c) mode =

(d) range =

(e) variance =

(f) standard deviation =

Rounding Rules:

• Mean, Standard Deviation, and Variance: Your answer should be rounded to one more decimal place than the raw data.

• Median: If you have to take the mean of two numbers then round that result to one more decimal place than the raw data. If one of the elements of the data set is the median, then use that number as is.

• Intermediate Steps: When performing intermediate steps to do something like calculate the standard deviation, it is best to round to at least one extra decimal place than will be used in the final answer.

Answer 1

The sample data is  11,     13,     5,     13,     7,     8

(a)

mean = ( 11 + 13 + 5 + 13 + 7 + 8) / 6 = 57/ 6 = 9.5

(b)

The sample is ascending order is 5, 7, 8, 11, 13, 13

n = number of elements = 6

As, n is even, median is equal to Mean on middle elements

= Mean of 3rd and 4th element

= (8 + 11)/2 = 19/2 = 9.5

(c)

The maximum frequency is for 13. It occurs for 2 times in the data.

So, mode = 13

(d)

Minimum element = 5

Maximum element = 13

Range = Maximum - Minimum = 13 - 5 = 8

(e)

Variance is given as,

where n = 6, and is the mean of the sample x.

So, variance = 11.1

(f)