Class 10 Math All topics Statistics

The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table:

Find the median length of the leaves.

Length (in mm) | Number of leaves |

$118−126$ $127−135$ $136−144$ $145−153$ $154−162$ $163−171$ $172−180$ | $3$ $5$ $9$ $12$ $5$ $4$ $2$ |

Solution:

Hence, median length $=146.75$ hours

The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to $(117.5−126.5,126.5−135.5,...,171.5−180.5.)$

Converting the given table into exclusive form and preparing the cumulative frequency table, we get

We have, $n=40$

$⇒2n =20$

The cumulative frequency just greater than $2n $ is $29$ and the corresponding class is $144.5−153.5$.

Thus, $144.5−153.5$ is the median class such that

$2n =20,l=144.5,cf=17,f=12$, and $h=9$

Substituting these values in the formula

Median, $M=l+⎝⎛ f2n −cf ⎠⎞ ×h$

$M=144.5+(1220−17 )×9$

$M=144.5+123 ×3=144.5+2.25=146.75$

Hence, median length $=146.75$ hours

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introduction to trigonometry

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introduction to trigonometry

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quadratic equations

surface areas and volumes

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