The following data are the temperatures of effluent at discharge from a sewage t

Question

The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days 50 49 51 46 46 49 49 51 50 52 48 51 50 51 38 45 49 47 52 45 46 48 Specify the classes, construct frequency distribution table, and find the following (do the calculation manually (do not use computer software)): a) Mean b) Median c) Mode d) Standard deviation e) Coefficient of variatiorn f First quartile g) Third quartile h) Draw a boxplot Note: benefit from this figure below to find outliers and extreme outliers from 1.5 Inter Quartile Range (IQR) as shown in the figure below

Explanation / Answer

a)
mean = sum of all number/ total number
= 1151/24
= 47.9583

b)
arrange the number in ascending order then find the middle number

Median = 49

c)
mode is the number which is most repeated

mode = 49 and 51

d)
standard deviation = summation of (x - mean)^2/n
= (38 - 47.9583)^2 + (44 - 47.9583)^2 + (44 - 47.9583)^2 + (45 - 47.9583)^2+................+ (52 - 47.9583)^2 +(52 - 47.9583)^2 / 24
= 3.2768
e)

Coefficient of variation = (std.dev / mean) * 100
= (3.2768 / 47.9583) * 100
= 6.8326%

f)
First quartile
38 , 44 , 44 , 45 , 45 , 46 , 46 , 46 , 47 , 48,48 , 49

g)
Third quartile
49 , 49 , 49 , 50 , 50 , 50 , 51 ,51 ,51 ,51 ,52 ,52,

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