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# The distribution below gives the weight of 30 students of a class. Find the median weight of the students.

Weight (in kg): | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 |

No. of students: | 2 | 3 | 8 | 6 | 6 | 3 | 2 |

Given:

The distribution gives the weight of 30 students in a class.

To do:

We have to find the median weight of students.

Solution:

Here,

$N = 30$

$\frac{N}{2} = \frac{30}{2} = 15$

The cumulative frequency just greater than $\frac{N}{2}$ is 19 and the corresponding class is 55 – 60.

This implies, that 55– 60 is the median class.

Therefore,

$l = 55, f = 6, F = 13$ and $h = (60 - 55) = 5$

Median $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$

$=55+\frac{15-13}{6} \times 5$

$=55+\frac{2}{6} \times 5$

$=55+\frac{5}{3}$

$= 55 + 1.67$

$= 56.67$

The median weight of students is 56.67 kg.

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