Question

Round all answers to three decimal places. The numbers of construction workers for various projects are 32 ,20 ,25 ,52 ,16 ,21 ,28 ,35 ,23 ,41 ,46 ,17 ,23 27 ,11 ,60

The mean of this data is:

The standard deviation of this data is:

The five number summary is:

The interquartile range is:

Replacing the largest number with (blank) results in the smallest whole number outlier

Answer 1

X	Mean, x̅	x-x̅	(x-x̅)²
32	29.8125	2.1875	4.78516
20	29.8125	-9.8125	96.28516
25	29.8125	-4.8125	23.16016
52	29.8125	22.1875	492.28516
16	29.8125	-13.8125	190.78516
21	29.8125	-8.8125	77.66016
28	29.8125	-1.8125	3.28516
35	29.8125	5.1875	26.91016
23	29.8125	-6.8125	46.41016
41	29.8125	11.1875	125.16016
46	29.8125	16.1875	262.03516
17	29.8125	-12.8125	164.16016
23	29.8125	-6.8125	46.41016
27	29.8125	-2.8125	7.91016
11	29.8125	-18.8125	353.91016
60	29.8125	30.1875	911.28516

∑x = 477

n = 16

∑(x-x̅)² = 2832.4375

Mean, x̅ = Ʃx/n = 477/16 = 29.813

Standard deviation, s = √(Ʃ(x-x̅)²/(n-1)) = √(2832.4375/(16-1)) = 13.742

Minimum = 11

First quartile, Q1 = 4.5th value of sorted data = 20.5

Median = 0.5(n+1)th value = 8.5th value of sorted data = 26

Third quartile, Q3 = 12.5th value of sorted data = 38

Maximum = 60

IQR = Q3 - Q1 = 38 - 20.5 = 17.5

Lower Fence = Q1 - 1.5*IQR = -5.75

Upper Fence = Q3 + 1.5*IQR = 64.25

Replacing the largest number with 65 results in the smallest whole number outlier.

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