Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

NCERT Math’s class 10 chapter 14

Page No. 293

Exercise 14.4

Question 2

# During the medical check-up of 35 students of a class, their weights were recorded as follows:

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It can be observed that the difference between two consecutive upper class limits is 2. The class marks with their respective frequencies are obtained as below.

Weight (in kg) Less than38 38-40 40-42 42-44 44 46 46-48 48-50 50-52 Total(n)

Frequency (f) 0 3-0=3 5-3=2 9-5=4 14-9=5 28-14=14 32-28=4 35-32=3 35

Cumulative

frequency 0 3 5 9 14 28 32 35

The cumulative frequency just greater than n/2 (i.e. 35/2 = 17.5) is 28, belonging to class intervals 46- 48.

Median class = 46 – 48

lower class limit (l) of median class = 46

Cumulative frequency (cf) of class preceding median class = 14

Class size (h) = 2

Median = l + ((n/2 – cf)/f) × h = 46 + ((17.5 – 14)/14) × 2 = 46 + 0.5 = 46.5

Therefore, median of this data is 46.5.

Hence, the value of median is verified.