Question

For what value of p, the following data will have same median and mode?
7 ,8,10, p, 11, 14, 16

Answer 1

Answer:

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 (

2

n

)

th

and (

2

n+2

)

th

.

∴ Here, median is the average of the values at (

2

34

)

th

or 17

th

position and (

2

34+2

)

th

or 18

th

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 17

th

position is 13 and at 18

th

position is 14.

∴Median=(

2

13+14

)=

2

27

=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.