Question

solve this as fast as possible​

Answer 1

Given :

• The median of the following data is 525.

• Total frequency = 100

To Find :

• Value of x and y = ?

Step-by-step explanation:

$\boxed{\begin{array}{cccc}\sf Class\: interval&\sf Frequency&\sf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 0-100&\sf 2&\sf 2 \\\\\sf 100-200 &\sf 5&\sf 7 \\\\\sf 200-300 &\sf x &\sf 7 + x \\\\\sf 300-400&\sf 12&\sf 19 + x\\\\\sf 400-500 &\sf 17 &\sf 36 + x \\\\\sf 500-600 &\sf 20 &\sf 56 + x \\\\\sf 600-700 &\sf y &\sf 56 + x + y \\\\\sf 700-800 &\sf 9 &\sf 65 + x + y \\\\\sf 800-900 &\sf 7 &\sf 72 + x + y \\\\\sf 900-1000 &\sf 4 &\sf 76 + x + y\end{array}}$

Median = 525

500 - 600 is median class.

Where,

• lower limit of median class (l) = 500

• Class interval (h) = 100 - 0 = 10

• n = 100

• Cumulative frequency of median (cf) = 36 + x

$\large{\boxed{\gray {\bf Median =\ l\ +\ \dfrac{\frac{n}{2}\ -\ cf}{f}\ \times\ h}}}\:$$\red\bigstar$

➨$\sf 525 =\ 500\ +\ \dfrac{\frac{100}{2}\ -\ \left(36\ +\ x\right)}{20}\ \times\ 100$

➨ 525 = 500 + (50 - (36 + x)) × 5

➨ 525 - 500 = (50 - 36 - x) × 5

➨ 25 = (14 - x) × 5

➨ 25 = 70 - 5x

➨ 5x = 70 - 25

➨ 5x = 45

➨ $\sf x = \dfrac{45}{5}$

➨ x = 9

Also

➨ $\sf \sum\:f_i = 76 + x + y$

➨ 100 = 76 + x + y

➨ 100 - 76 = 9 + y

➨ 24 = 9 + y

➨ y = 24 - 9

➨ y = 15

Therefore, the value of x and y are 9 and 15 respectively.