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Question
Calculate the A.M and S. D for the following distribution :
Class:0−1010−2020−3030−4040−5050−6060−7070−80Frequency:1816151210521
Calculate the A.M and S. D for the following distribution :
Class:0−1010−2020−3030−4040−5050−6060−7070−80Frequency:1816151210521
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Solution
CIfxu=(x−A)/hfuu2fu20−10185−3−54916210−201615−2−3246420−301525−1−1511530−401235000040−50104511011050−6055521042060−702653691870−8017544161679−71305
Here, N= 79, A = 35 , ∑fiui=−71,∑fiu2i=305 and h=10
∴ Mean = ¯¯¯x=A+h(1N∑fiui)
⇒¯¯¯x=35+10(−7179) = 26.01
var(x)=h2[1N∑fiu2i−(1N∑fiui)2]=100[30579−(−7179)2]=305.30
∴ S. D = √var(x)=√305.30=17.47
CIfxu=(x−A)/hfuu2fu20−10185−3−54916210−201615−2−3246420−301525−1−1511530−401235000040−50104511011050−6055521042060−702653691870−8017544161679−71305
Here, N= 79, A = 35 , ∑fiui=−71,∑fiu2i=305 and h=10
∴ Mean = ¯¯¯x=A+h(1N∑fiui)
⇒¯¯¯x=35+10(−7179) = 26.01
var(x)=h2[1N∑fiu2i−(1N∑fiui)2]=100[30579−(−7179)2]=305.30
∴ S. D = √var(x)=√305.30=17.47
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