Question

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Answer 1

Sr, No	X	(X - X̄)²		sorted X
1	18.71	4.233		18.04
2	21.41	0.413		18.71
3	20.72	0.002		18.92
4	21.81	1.087		19.25
5	19.29	2.183		19.29
6	22.43	2.764		19.44
7	20.17	0.357		19.77
8	23.71	8.658		20.17
9	19.44	1.762		20.33
10	20.5	0.072		20.5
11	18.92	3.413		20.72
12	20.33	0.191		21.12
13	23	4.984		21.41
14	22.85	4.337		21.77
15	19.25	2.303		21.81
16	21.77	1.005		22.11
17	22.11	1.802		22.43
18	19.77	0.995		22.85
19	18.04	7.439		23
20	21.12	0.124		23.71

	X	(X - X̄)²
total sum	415.35	48.125375
n	20	20

a)

mean =    ΣX/n =    20.7675
b)

Median = (n+1)/2 = 10.5th value of sorted data

so, median = 20.61

c)

10% trimmed mean

20 numbers are there

10% 0f 20 = 2

so removing the two lowest and two highest numbers and take their average

18.92
19.25
19.29
19.44
19.77
20.17
20.33
20.5
20.72
21.12
21.41
21.77
21.81
22.11
22.43
22.85

10% trimmed mean= 20.7431

d)

Q1=1/4(n+1)=21/4=5.25th value = 19.29+(19.29-19.44)*0.25=19.3275

Q3=0.75(n+1)=15.75th value = 21.81+0.75*(22.11-21.81)=22.035

e)

IQR = Q3-Q1 = 2.7075

f)

lower bound=Q1-1.5IQR = 15.26625

g) upper bound = Q3+1.5*IQR = 26.0962

h)

i)

maximum=23.71

j) minimum=18.04

k) Range=5.67

l) sample variance =    Σ(X - X̄)²/(n-1)=   2.533

m) sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   1.5915