# Ststistics

Submitted By khorshedraju
Words 327
Pages 2
Exercises: 02
21, 22, 22, 22, 22, 23, 27, 28, 29, 33, 36, 36
Regarding the twelve observations as the population of interest, we have N=12 so, their Mean:
"μ=" ∑_(i=1)^N▒X_i "/N"

=(21+22+22+22+22+23+27+28+29+33+36+36)/12
=26.75
Median:
=(n/2+(n+2)/2)/2

=(12/2+(12+2)/2)/2 =6.5th position
6th +7th /2=25 Mode:
The mode of these percentage assessment rates is 22.

Midhinge :
=(Q1+Q3)/2
=(22+31)/2
=26.5
Midrange:
=(Highest data+lowest data)/2
=(21+36)/2
=28.5 Harmonic mean:
H=12/(1/21+1/22+1/22+1/22+1/22+1/23+1/27+1/28+1/29+1/33+1/36+1/36)
=12/0.466008157
=25.75
Geometric mean:
G=√(12&21*22*22*22*22*23*27*28*29*33*36*36)
=26.23 Range:
Maximum data-minimum data
36-21=15
IQR:
=Quartile3 –Quartile 1
=9

Population Variance: σ^2=(∑_(i=1)^N▒〖(x-μ)〗^2 )/N
=354.2525/12
=29.52 Sample variance: s^2=(∑_(i=1)^n▒(x-x ̅ )^2 )/(n-1)
=354.2525/(12-1)
=32.20 Population Standard Deviation: σ=√((∑_(i=1)^N▒(x-μ)^2 )/N)
=5.43
Sample Standard Deviation: s=√((∑_(i=1)^n▒(x-x ̅ )^2 )/(n-1))
=5.67

Population Co-efficient of Variation:
= σ/μ*100
=20.31
Sample Co-efficient of Variation:

=s/□(←┬x )*100
= 21.21

x μ 〖(x-μ)〗^ 〖(x-μ)〗^2
21 26.75 -5.75 33.0625
22 26.75 22.5625
22 26.75 22.5625
22 26.75 22.5625
22 26.75 22.5625
23 26.75 14.0625
27 26.75 0.0625
28 26.75 1.5625
29 26.75 5.0625
33 26.75 39.0625
36 26.75 85.5625
36 26.75 85.5625…...

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