The length of 40 leaves of a plant are measured correct to the nearest millimeter- and the data obtained is represented in the following table- begin array - Whline118-126-3Whline127-135-5Whline136-144-9Whline145-153-12Whline 154-162-5Whline 163-171-4Whline172-180 -2Whline end array Find the median length of leaves-

The correct option is C 146.75[ C.I amp;Frequency amp;C.F; 118 126 amp;3 amp;3; 127 135 amp;5 amp;8 ...

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Mathematics

Ogive of Less Than Type

The length of...

Question

The length of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table.

$\begin{matrix} Length (in mm) & Number of leaves 118 - 126 & 3 127 - 135 & 5 136 - 144 & 9 145 - 153 & 12 154 - 162 & 5 163 - 171 & 4 172 - 180 & 2 \end{matrix}$

Find the median length of leaves.

123.45

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143.55

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146.75

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134.75

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Solution

The correct option is C 146.75
$\begin{matrix} C.I & Frequency & C.F 118 - 126 & 3 & 3 127 - 135 & 5 & 8 136 - 144 & 9 & 17 145 - 153 & 12 & 29 154 - 162 & 5 & 34 163 - 171 & 4 & 38 172 - 180 & 2 & 40 \end{matrix}$

We have, n = 40 & $\frac{n}{2} = 20$
hence, median class $= 145 - 153$

Now, We see the 20th Observation on the graph by extending it to the ogive.

$∴$ the value for median seen from the Graph is 146.75.

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