EX 13.3 (Question: 7)

EX 13.3 (Question: 7) 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: Given data: Total 𝑛=30 𝑛/2=15 Median class = 55 – 60 (since cumulative frequency just greater than 50 is 78) 𝑙 = 55 (lower limit) 𝐹 = 13 (cumulative frequency before median class) 𝑓 = 6 (frequency of median class) ℎ = 60 − 55= 5 (class width) Using formula: Median = 𝑙 + ( "n/2−F" /"𝑓" )"×h" Where: 𝑙 = 55, 𝐹 = 13, 𝑓 = 6, ℎ = 5. Median = 55 + ("(15−13" /6)"× 5" "=" 55 + 2/6 "× 5" "=" 55 + 10/6 "= 55+1.67" =56.67kg The median weight of the students is approximately 56.67kg

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