a.
Class10−1313−1616−1919−2222−25f4612144m11.514.517.520.523.5d−2−1012f⋅d−8−60148f⋅d216601416cf410223640
A=17.5
d=hx−A,h=3
Mean=xˉ=A+n∑fd⋅h=17.5+408⋅3=18.1The median class is 16-19.
L=16,n=40
Cumulative frequency of the class preceding the median class cf=10
Frequency of the median class f=12
Class length of median class c=3
Median M=L+f2n−cf⋅c=16+12240−10⋅3=18.5
Maximum frequency is14.
The mode class is 19-22.
L=19
Cumulative frequency of the class preceding the median class cf=10
Frequency of the mode class f1=14
Frequency of the preceding class f0=12
Frequency of the succeeding class f2=4
Class length of mode class c=3
Z=L+2f1−f0−f2f1−f0⋅c=19+2(14)−12−414−12⋅3=19.5b.
Range=222+25−210+13=12S2=n−1∑f⋅d2−n(∑f⋅d)2⋅h2=40−152−40(8)2⋅32=13151.2≈11.63077S=S2=13151.2≈3.4104c.
Coefficient of Variation=xˉS⋅100%=18.113151.2⋅100%≈18.842%d.
Class with (4n)th value of the observation in cf column
=(440)th value of the observation in cf column
=(10)th value of the observation in cf column
and it lies in the class 13-16.
Q1 class: 13−16
L=13
Q1=L+f4n−cf⋅c=13+6440−4⋅3=16Class with (43n)th value of the observation in cf column
=(43⋅40)th value of the observation in cf column
=(30)th value of the observation in cf column
and it lies in the class 19-22.
Q3 class: 19−22
L=19
Q3=L+f43n−cf⋅c=19+1443⋅40−22⋅3≈20.7143IQR=Q3−Q1≈20.7143−16≈4.7143
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