Question

2. If the median of the distribution given below is 28.5, find the values of x and y.
Class interval
Frequency
0 - 10
5
10 - 20
20 - 30
20
30 - 40
15
40 - 50
у
50 - 60
5
Total
60​

Answer 1

☯ Median is given which is 28.5.

$\boxed{\begin{array}{cccc}\sf Class\: Interval &\sf Frequency&\sf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 0 - 10 &\sf 5 &\sf 5 \\\\\sf 10 - 20 &\sf x &\sf 5+x \\\\\sf 20 - 30 &\sf 20 &\sf 25+x \\\\\sf 30 - 40 &\sf 15 &\sf 40+x \\\\\sf 40 - 50 &\sf y &\sf 40+x+y \\\\\sf 50 - 60 &\sf 5 &\sf 45 + x + y \\\\\sf Total &\sf n = 60 &\sf\end{array}}$⠀⠀

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Median = l + \dfrac{\frac{n}{2} - CF}{f} \times h}}}}$

Here,

• $\sf n = \sum f = \bf{60}$

• $\sf \frac{n}{2} = \frac{\cancel{60}}{\cancel{\: 2}} = \bf{30}$

• $\sf l = Lower\:limit\:of\;class = \bf{20}$

• $\sf CF = Cumulative\: frequency = \bf{5 +x}$

• $\sf f = Frequency\:of\:median\;class = \bf{20}$⠀

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\dag\;{\underline{\sf{Now,\:Putting\:values\:in\:formula,}}}$

$:\implies\sf Median = l + \dfrac{ \frac{n}{2} - cf}{f} \times h \\\\\\:\implies\sf 28.5 = 20 + \dfrac{30 - (5 + x)}{20} \times 10 \\\\\\:\implies\sf 28.5 = 20 + \dfrac{25 - x}{2}\\\\\\:\implies\sf 28.5 - 20 = \dfrac{25 - x}{2}\\\\\\:\implies\sf 8.5 = \dfrac{25 - x}{2}\\\\\\:\implies\sf 8.5 \times 2 = 25 - x\\\\\\:\implies\sf 17 = 25 - x\\\\\\:\implies\sf x = 25 - 7\\\\\\:\implies\boxed{\frak{\pink{ x = 8}}}$

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And,

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$:\implies\sf 45 + x + y = 60 \\\\\\:\implies\sf y = 60 - 45 - x \\\\\\:\implies\sf 15 - 8 \\\\\\:\implies\boxed{\frak{\pink{y = 7}}}$

$\therefore\:{\underline{\sf{Hence,\:the \ required \ Values \ of \ x \ and \ y \ is \ {\textsf{\textbf{8 \& \ 7}}}.}}}$

Answer 2

Refer The Attachment ⬆️

$\red{\sf{✯\; MrMonarque}}$

Hope It Helps You ✌️