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Question

dentify the outlier in the data set. Then find the mean, median, mode(s), range and standard deviation when the outlier is included and when it is not.
15,18,20,26,18,62

Answer 1

15 ,18, 20 , 26, 18 , 62.

Mean : -

Mean is the ratio between sum of the total numbers and total given numbers

Mean = ( 15 +18+ 20+26+ 18+ 62) / 6.

Mean=159/6

Mean=26.5

Median :-

15 ,18, 20 , 26, 18 , 62.

To find the median , we must need to put the numbers in order from smallest to largest.

15 ,18, 18, 20 , 26, 62.

Median is the arithmetic mean of two middle most numbers = (18+20)/2 = 38/2 =19

So the median is 19.

Mode :-

The mode is  the value which occures most often in a data.

15 ,18, 20 , 26, 18 , 62.

This is the  most common value 18.

So we say 18 is the mode.

Range : -

The range is the different between the largest and smallest value in data  in this case 62 and15

So the range is 62 - 15  = 47.

Standard deviation : -

15 ,18, 20 , 26, 18 , 62.

 Mean = 26.5

To caliculate the numbers  deviation  first  compute difference of each data point

from the mean ,and sqare the result of each.

(15 - 26.55)^2 = (-11.5)^2 = 132.25

(18 - 26.5)^2  = (-8.5)^2 = 72.25

(20 - 26.5)^2 =(-6.5)^2 = 42.25

(26 - 26.5)^2 =(0.5)^2 = 0.25

(18 - 26.5)^2 = (-8.5)^2 = 72.25

(62 - 26.5)^2 = (35.5)^2 = 1260.25

Next ,compute the mean of these values and take the square root.

= (132.5 + 72.25 + 42.25+ 0.25 + 72.25 + 1260.25)/6

= (1579.75) / 6

= 263.29

Sqrt(263.29) = 16.2262

standard deviation of given numbers is 16.23.

Solution : Mean =26.5, Median= 19, mode =18, Range =47 , Standard deviation=16.23.