The ages of ten patients admitted at a hospital for covid-19 were 8,5,14,X, 8,Y,11,9,8&7 yrs. Use the data to answer the following question.

Question

I NEED HELP WITH THESE QUESTION PLEASE 

The ages of ten patients admitted at a hospital for covid-19 were 8,5,14,X, 8,Y,11,9,8&7 yrs. Use the data to answer the following question.

A). Given that the average age of these patients is 10 years and the value of Y is twice the value of X, what are the values of X and Y​​​​​​.

B). What is the median age of these patients.

C). Describe the distribution of these ages.

D). Calculate the appropriate measure of variation for these ages.

Answer 1

(A) Average = 10 years (Given) and y = 2x

\(\therefore \frac{8 + 5+ 14 + x + 8 + y + 11+ 9 + 8 + 7}{10}= 10\)

⇒ \(70 + x +y = 100\)

⇒ \(x + 4 = 30\)

⇒ \(x + 2x = 30\)

⇒ \(x = \frac{30}3 = 10 \) years

& \(y = 2 \times 10 = 20\) years

(B) Increasing order of ages of these patients are 5, 7, 8, 8, 8, 9, 10, 11, 14, 20

n = 10 when is even

\(\therefore \) Median = \(\frac{\frac{10}2th \,term + (\frac{10}2 + 1)th\,term}2\)

\(= \frac{8 + 9}2\)

\(= 8.5\)

(C) 

Ages	5	7	8	9	10	11	14	20
No. of patients	1	1	3	1	1	1	1	1

(D) Mean \( = \frac{\sum X}n =\frac{100}{10} = 10\)

Variance \(=\frac{\sum X^2}n - 10^2\)

\(= \frac{25 + 49 + 64 \times 3 + 81 + 100 + 121 + 196 + 400}{10}-100\)

\( =\frac{1164}{10} - 100\)

\(= 116.4 - 100\)

\(= 16.4\)