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The median of the given data is $28.5$.
Find the values of $a$ and $b$.
| Class | Frequency |
|---|---|
| $0-10$ | $5$ |
| $10-20$ | $a$ |
| $20-30$ | $20$ |
| $30-40$ | $15$ |
| $40-50$ | $b$ |
| $50-60$ | $5$ |
| Total | $60$ |
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Solution:
Class | Frequency | Cumulative Frequency(cf)
$0-10$ | $5$ | $5$
$10-20$ | $a$ | $5+a$
$20-30$ | $20$ | $25+a$
$30-40$ | $15$ | $40+a$
$40-50$ | $b$ | $40+a+b$
$50-60$ | $5$ | $45+a+b$
Total | $60$
For Correct cf (1 Mark)
$45+a+b = 60$
$a+b = 15$ -----(i) (1 Mark)
Median class $= 20 - 30$, $N = 60$
$28.5 = 20 + \frac{30-(5+a)}{20} \times 10$ (1 Mark)
$28.5 = 20 + \frac{25-a}{2}$ (1/2 Mark)
$a = 8$ (1/2 Mark)
and $b = 7$ [from (i)] (1/2 Mark)
Class | Frequency | Cumulative Frequency(cf)
$0-10$ | $5$ | $5$
$10-20$ | $a$ | $5+a$
$20-30$ | $20$ | $25+a$
$30-40$ | $15$ | $40+a$
$40-50$ | $b$ | $40+a+b$
$50-60$ | $5$ | $45+a+b$
Total | $60$
For Correct cf (1 Mark)
$45+a+b = 60$
$a+b = 15$ -----(i) (1 Mark)
Median class $= 20 - 30$, $N = 60$
$28.5 = 20 + \frac{30-(5+a)}{20} \times 10$ (1 Mark)
$28.5 = 20 + \frac{25-a}{2}$ (1/2 Mark)
$a = 8$ (1/2 Mark)
and $b = 7$ [from (i)] (1/2 Mark)