Question

Find the median of 24, 33, a, a-1, 12, 16 if mean of 10,20,30,40 and 50 is a.​

Answer 1

Answer:

26.5

Step-by-step explanation

mean of 10,20,30,40,50 comes out to be 30 that is 150/5

so a=30 a-1=29

median

12,16,24,29,30,33

median will be average of 24 and 29

that is 53/2=26.5

Answer 2

Here, we do not have the value for variable a. So, we will find it first

Mean of 10, 20, 30, 40, 50= $\frac{10+20+30+40+50}{5}$

⇒$a=\frac{150}{5}$

⇒$a=30$

Value of a= 30

Value of a-1= 30-1= 29

Nos. of which the median is to be found= 24, 33, a, a-1, 12, 16 or 24, 33, 30, 29, 12, 16

Arranging the data in ascending order, we have

12, 16, 24, 29, 30, 33.

Here, we have even number of observations, i.e. 6. So, median will be mean of the middlemost two observations.

Here, n=6                             (n=number of observations)

Median= $\frac{\frac{n}{2}^{th} term +(\frac{n}{2}+1)^{th} term }{2}$

⇒Median= $\frac{\frac{6}{2}^{th} term+ (\frac{6}{2}+1)^{th} term }{2}$

⇒Median= $\frac{3^{rd}term +4^{th}term }{2}$

⇒Median= $\frac{24+29}{2}$

⇒Median= $\frac{53}{2}$

⇒Median= 26.5