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Ungrouped Frequency Distribution Table

The median of...

Question

The median of the data in the following table is $27$ . Find the missing frequencies $f_{1}$ and $f_{2}$

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Solution

Class*frequency (Cf)

$5$
$5 + f_{1}$
$25 + f_{1}$
$39 + f_{1}$
$39 + f_{1} + f_{2}$
$47 + f_{1} + f_{2}$

$47 + f_{1} + f_{2} = 68 \Rightarrow f_{1} + f_{2} = 21$ ...(1)

$m = L + (\frac{\frac{n}{2} - C f}{f}) \times h$

$27 = 20 + (\frac{34 - (5 + f_{1})}{20}) \times 10$

$7 = (\frac{34 - (5 + f_{1})}{2})$

$7 = 17 - (\frac{5 + f_{1}}{2})$

$\frac{5 + f_{1}}{2} = 17 - 7 = 10$

$5 + f_{1} = 20$

$∴ f_{1} = 15$

From (1)

$f_{2} = 21 - f_{1} = 21 - 15$

$∴ f_{2} = 6$

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