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Question

Calculate the mean and the median for the following continuous frequency distributions.

Class0−1010−2020−3030−4040−5050−6060−70fi68202515104


A

34.25, 32.4

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B

34.20, 32.4

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C

34.20, 32.1

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D

34, 32.1

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Solution

The correct option is B

34.20, 32.4


Class010102020303040405050606070fi68202515104c.fi6143459748488

Mean: To calculate the mean, we calculate ni=1xi fi for each observation and divide by ni=1fi

ni=1xifi=5(6)+15(8)+25(20)+35(25)+45(15)+55(10)+65(40)

=30+120+500+875+675+550+260

=3010

¯x=7i1xifi7i=1fi=301088=34.20=mean

Median: To calculate the median for a continuous frequency lies and apply the formula1

Median=l+((N2)cf× h)

l lower limit of median class

N sum of frequencies

c cumulative frequency of class precending median class

f frequency of median class

h width of median class

In the given example,

Median class=30-40 {because(882)thterm lies in 3040 class}

l=30

N=7i=1fi=88

C=34

f=25

h=10

Median=M=30+ =((802)3425)× 10

=30+(625)10=30+24=32.4.


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