Question

orphanage. He is left with 3200. Find his income.
(iv) The mean of observations-18. 14. 15. 19. 15, a. 12, 15 and 16 is.16. Find the value of
a. Then find the median and mode.
citen below-​

Answer 1

Answer:

Value of a = 20

Median = 15

Mean = 15

Step-by-step explanation:

We are given the mean of following data;

 18, 14, 15, 19, 15, a, 12, 15 and 16

Mean formula is = Sum of all values ÷ Number of observations

                  16     = $\frac{18+ 14+ 15+ 19+ 15+ a+ 12+ 15+ 16}{9}$

                  16     = $\frac{124+a}{9}$

                  124 + a = 16 * 9

                    a = 144 - 124 = 20

So, value of a = 20 .

Now arranging the data in ascending order;

 12, 14, 15, 15, 15, 16, 18, 19, 20

• Calculation median ;      

        Number of observation is odd i.e. 9

So, median formula is given by = $(\frac{n+1}{2} )^{th}$ obs.

        Median = $(\frac{9+1}{2} )^{th}$ obs = 5th observation

Therefore, Median = 15 .

• Calculating Mode ;

        Mode is given by the number which appears maximum number of

        times in our data. So, in our data since 15 is coming maximum no. of

        times i.e. 3 .

Therefore, Mode of data is 15 .