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Question

For a frequency distribution consisting of 18 observations, the mean and the standard deviation were found to be 7 and 4 respectively. But on comparison with the original data, it was found that a figure 12 was miscopied as 21 in calculations. Find the correct mean and standard deviation.___

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Solution

Given xi18=7( mean =7 and n=18)
xi=18×7=126

Since an observation 12 was miscopied as 21, therefore,

correct xi=12621+12=117

Hence true mean =correct xi18=11718=6.5

Also variance is given to be 42=16,

therefore, x2i18(mean)2=16

x2i18=42+(mean)2=16+72

x2i=18(16+49)=1170

But, in the summation on R.H.S., one observation (=12) was miscopied as 21, therefore,

correct x2i=1170212+122=1170441+144=873.

Hence true variance =correctx2i18(true mean)2

=87318(6.5)2=48.542.25=6.25

True S.D=true variance=6.25=2.5

Correct mean =6.5 and
correct standard Deviation =2.5


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