Question

The mean of the numbers 21, 30, 16, x, and 9 is 18 The median of the numbers 23, 30, 31, 3x, 3x + y, 60, 67, and 69 is 47.5. What is the value of y?

Answer 1

☆ Elucidation :-

We know that, mean of some given numbers is :-

$\sf: \implies \: \frac{sum \: of \: all \: numbers}{number \: of \: observations}$

Therefore, we have been provided with,

• Number of observation = 5
• Sum of all numbers = 76 + x
• Mean of these numbers = 18

Therefore, According to the question and the information provided, we get,

$\sf: \implies \: 18 = \frac{76 + x}{5} \: \: \: \: \: \: \: \\ \sf: \implies \: 76 + x = 18 \times 5 \\ \sf: \implies \: x = 90 - 76 \: \: \: \: \: \: \: \: \\ \sf: \implies \: x = 14 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

∴ The value of x is 14.

Now, we can easily put the value of x in the second case and find out the value of y. So,

Now, in second case,

• Sum of all the number = 364 + y
• Number of observation = 8
• Mean of the given numbers = 47.5

Therefore, according to the question and the given information,

$\sf: \implies \: 47.5 = \frac{364 + y}{8} \: \: \: \: \: \: \: \\ \sf: \implies \:364 + y = 47.5 \times 8 \\ \sf: \implies \: y = 380 - 364 \: \: \: \: \: \: \: \: \: \\ \sf: \implies \: y = 16 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the value of y is $\boxed{ \sf \: 16}$

Hope that helps ^_^

Answer 2

Answer:

Step-by-step explanation:

First we find the value of x.

Mean = Sum of all the observation / Total Number of Observation

18 = 21+ 30 + 16 + x + 9 / 5

90 = 76 + x

x = 90 -76

x = 14

Now, In second data;

Total no. of observation is 8 so by n/2= 8/2 = 4th observation

Median = 4th + 5th / 2

47.5 = 3x + 3x + y / 2

95 = 6 X 14 + y

95 - 84 = y

y = 11 ans

Hope it Helpzz.

Solution given by Haritha Bharath is wrong... Mine solution is write. In place of 47.5 he wrotes 47.