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The distribution below gives the weights of 30 students of a class. Find the median weight of the students. - CBSE Class 10 - Mathematics

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Question

The distribution below gives the weights 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
Number of students 2 3 8 6 6 3 2

Solution

The cumulative frequencies with their respective class intervals are as follows

Weight (in kg) Frequency (fi) Cumulative frequency
40 − 45 2 2
45 − 50 3 2 + 3 = 5
50 − 55 8 5 + 8 = 13
55 − 60 6 13 + 6 = 19
60 − 65 6 19 + 6 = 25
65 − 70 3 25 + 3 = 28
70 − 75 2 28 + 2 = 30
Total (n) 30  

Cumulative frequency just greater than n/2 (i.e 30/2 = 15) is 19, belonging to class interval 55 − 60.

Median class = 55 − 60

Lower limit (l) of median class = 55

Frequency (f) of median class = 6

Cumulative frequency (cf) of median class = 13

Class size (h) = 5

`"Median" = l +((n/2-cf)/f)xxh`

= 55+((15-13)/6)xx5

=55+10/6

= 56.67

Therefore median weight is 56.67 kg

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 14: Statistics
Ex.14.30 | Q: 7 | Page no. 289
Solution The distribution below gives the weights of 30 students of a class. Find the median weight of the students. Concept: Median of Grouped Data.
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