Question

find the median of the following data 19 , 25 , 59 , 48 , 35 , 31 , 30 , 32 , 51.if 25 is replaced by 52 , what will be the new median

Answer 1

Given that,
19,25,59,48,35,31,30,32,51.

( put all of the values into order, median is the middle value).

19,25,30,31,32,35,48,51,59.

median = 32.

if 25 is replaced by 52, ie,

19,30,31,32,35,48,51,52,59.

median = 35.

Answer 2

Answer:

Median :32

New Median: 35

Step-by-step explanation:

Data :  19 , 25 , 59 , 48 , 35 , 31 , 30 , 32 , 51.

Arrange the data in ascending order

19, 25, 30,31 ,32 , 35 ,48,51 ,59

No. of observations n  = 9 (odd)

Median = $\frac{n+1}{2} \text{th term}$

            = $\frac{9+1}{2}\text{th term}$

            = $\frac{10}{2}\text{th term}$

            = $5\text{th term}$

            = $32$

Now we are given that 25 is replaced by 52

So, New data : 19, 52 30,31 ,32 , 35 ,48,51 ,59

Arrange in ascending order

19, 30, 31 , 32 , 35 ,48 , 51 , 52 ,59

No. of observations n  = 9 (odd)

Median = $\frac{n+1}{2} \text{th term}$

            = $\frac{9+1}{2}\text{th term}$

            = $\frac{10}{2}\text{th term}$

            = $5\text{th term}$

            = $35$

Hence the new median is 35