Question

The number of words defined on pages randomly selected from a dictionary are given below. Find the range and standard deviation for the set of numbers.
65, 59, 43, 43, 40, 63, 71, 77, 31, 64

Answer 1

Answer: The range of the set of numbers is 46 and the standard deviation is 14.44 .

Explanation:

In is given that the observations are 65, 59, 43, 43, 40, 63, 71, 77, 31, 64.

From given data it is noticed that the highest observation is 77 and the lowest observation is 31.

Range = Highest observation - Lowest observation

Range = 77 - 31 = 46

To find the standard deviation, first we have to find the mean.

$\text{Mean}={\frac{\text{Sum of observation}}{\text{Total number of observations}}$

Total of the observations is 556 and number of observation is 10.

$\text{Mean}=\frac{556}{10}=55.6$

Formula fr standard deviation is,

$\sigma =\sqrt{\frac{\sum (x-mean)^2}{n}}$

To find the above values form a table as shown below.

$\sigma =\sqrt{\frac{2086.4}{10}}$

$\sigma =\sqrt{208.64}$

$\sigma =14.44$

Therefore, the range of the set of numbers is 46 and the standard deviation is 14.44 .