Question

How do you find the mean, median, and mode of the following frequency distribution table?

Score* (Number of Students)
10 - 6
9 - 13
8 - 12
7 - 11
6 - 13
5 - 5

Answer 1

`"Mean "bar(X)=67.55 ," Median " M=8 and "Mode "Z=13`

Explanation:

Let us ordering the data from least to greatest.

Please see the table given below.

Let ,

`x_i="Score" and f_i="Number of students"`

`N="Total Number of students"`

`and Cf_i="Comulative frequency"`

`color(red)((1)"Mean " bar(X)=(sum f_ix_i)/N =(453)/60=67.55`

`"Median " M=((N+1)/2)th " score"to x_i`

`"Median " M=((60+1)/2)th " score"tox_i`

`"Median " M=((30.5)th " score"tox_i`

Now ,from `Cf_ito29 < 30.5 , and 30.5 > 41`

So, see the cell in the green color :

`color(green)(Cf_i=41to "for "x_i=8`

`:."Median " M=8`

`(3)" Mode " Z="Frequency repeated in the set of data,"`
`color(white)((3)" Mode " Z=)"maximum number of times"`

`:.color(orange)(" Mode " Z=13to"see the yellow color in table for "f_i.`

`i.e." Mode " Z=13`

Hence ,

`"Mean "bar(X)=67.55 ," Median " M=8 and "Mode "Z=13`