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Question

Find the mean deviation from the mean for the following data :

(i) xi579101215fi862226

(ii) xi510152025fi74635

(iii) xi1030507090fi42428168

(iv) Size2021222324Frequency64514

(v) Size13579111315Frequency334147434

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Solution

xifiCF|xiM|fi|xiM|588|57|=2167614|77|=0009216|97|=20410218|107|=30612220|127|=51015626|157|=848Totalfi=26fi|xiM|=84

Here, N=fi=26 even

Median M=N2th observation+(N2+1)th observation2

262th observation+(262+1)th observation2

=13th observation + 14th observation2

Mean deviation about median =fi|xiM|fi=8426=3.23

xififixi|xi¯x|fi|xi¯x|5735|514|=96310440|1014|=41615690|1514|=10620360|2014|=618255125|2514|=1155Totalfi=25350158

Mean ¯=fixifi=35025=14

Mean deviation about mean =fi|xi¯x|fi=15825=6.32

xififixi|xi¯x|fi|xi¯x|10440|1050|=401603024720|3050|=2048050281400|5050|=0000070161120|7050|=20320908720|9050|=40320Totalfi=80fixi=40001280

Mean ¯=fixifi=400080=50

Mean deviation about mean =fi|xi¯x|fi=128080=16

SizeFrequencyfixidi=|xix|fidi2061201.659.90214840.652.602251100.351.75231231.351.35244962.359.40Total2043325
Now, ¯x=fixifi=43320=21.65
M.D.=fi|xi¯x|fi=2520=1.25

xififixi|xi¯x||xi8|fi|xi¯x|133|18|=721339|38|=5155420|58|=31271498|78|=1149763|98|=1711444|118|=31213339|138|=51515460|158|=728Totalfi=42fixi=336124

Now, ¯x=fixifi=33642=8

M.D.=fi|xi¯x|fi=12442=2.95


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