Question

A sample of size n = 10 n=10 is drawn from a population. The data is shown below. 98.8 110.5 117.2 100.2 135.2 135.2 135.2 115.8 125.8 106.6 What is the range of this data set?

range =

What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, reporting 2 more decimal places than the original data. Please, please, please do not calculate the value by hand.

stdev =

Answer 1

Range is the subtraction of largest observation to the smallest observation i.e.,

Range = Largest observation - smallest observation

From the data, largest observation is 135.2

and smallest data is 98.8

So, range = 135.2-98.8 = 36.4

Therefore, range is 36.4

Standard deviation of a sample is given as,

First find mean of the data,

  

98.8	-19.25	370.5625
110.5	-7.55	57.0025
117.2	-0.85	0.7225
100.2	-17.85	318.6225
135.2	17.15	294.1225
135.2	17.15	294.1225
135.2	17.15	294.1225
115.8	-2.25	5.0625
125.8	7.75	60.0625
106.6	-11.45	131.1025

Total 1825.505

Therefore, standard deviation is 14.242

This can also be obtain using R software as,

First define the data in vector form as

x<-c(98.8 ,110.5, 117.2, 100.2, 135.2, 135.2, 135.2, 115.8, 125.8, 106.6)

Now using function range() and sd() we can find our desire result

range(x) ## this will give the smallest and largest observation

98.8 135.2

sd(x) ## this will give standard deviation of the sample

14.24198