Question

Q8. Calculate range, median and mode for the following data.
12, 15, 12, 13, 5, 6, 10, 20, 12, 11, 8, 10, 6​

Answer 1

Answer:

X 10 11 12 13 14 15

F 1 4 7 5 9 8

For a frequency distribution,

So, total number of observation =

=(1+4+7+5+9+8)=34

It is a even number.

So, median is the value of average of values at

$( \frac{n}{2} )$

And

$(n \ + \frac{2th}{2})$

∴ Here, median is the average of the values at

$( \frac{n}{2} ) {}^{th}$

or 17th position and

$(3 \ + \frac{2}{2} )th$

or 18th position

X 10 11 12 13 14 15

F 1 4 7 5 9 8

position

1 1+4=5 5+7=12 12+5=17 17+9=26 26+8=34

So, value of x at 17th position is 13 and at 18th position is 14.

∴Median

$\frac{13}{2} + {}^{14} = \frac{27}{2} = 13.5.$

Mode for a frequency distribution is the value which is the most common frequent value.

Here 14 has frequency 9 which is highest. So, mode for the frequency distribution is 14.