A survey of heights in cm of 51 girls of class X of a school was conducted and the following data was obtained- Find the median height- HEIGHT IN CM NUMBER OF GIRLS BELOW 140 4 140-145 7 145-150 18 150-155 11 155-160 6 160-165 5

[ CLASS INTERVALS amp; FREQUENCY amp; CUMULATIVE FREQUENCY; BELOW 140 amp; 4 amp; 4; ...

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Standard X

Mathematics

Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

A survey of h...

Question

A survey of heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height.

$\begin{matrix} H E I G H T (I N C M) & N U M B E R O F G I R L S B E L O W 140 & 4 140 - 145 & 7 145 - 150 & 18 150 - 155 & 11 155 - 160 & 6 160 - 165 & 5 \end{matrix}$

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Solution

$\begin{matrix} CLASS INTERVALS & FREQUENCY & CUMULATIVE FREQUENCY B E L O W 140 & 4 & 4 140 - 145 & 7 & 11 145 - 150 & 18 & 29 150 - 155 & 11 & 40 155 - 160 & 6 & 46 160 - 165 & 5 & 51 CUMULATIVE FREQUENCY & 51 \end{matrix}$

n = 51

$(\frac{n}{2}) = 25.5$

So, the cumulative frequency of class is corresponding to class-interval 145-150.

l (lower limit) =145,

Cumulative frequency of class preceding 145-150 = 11

f (frequency of median class) = 18

h (size of class-interval) = 5

Median $= l + (\frac{\frac{n}{2} - 1}{f}) h = 145 + (\frac{25.5 - 11}{18}) \times 5 = 149.03$

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A survey of heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height. HEIGHT (IN CM)NUMBER OF GIRLSBELOW 1404140−1457145−15018150−15511155−1606160−1655