Q) Medical check-up was carried out for 35 students of a class and their weights were recorded as follows:
Find the difference between the mean weight and the median weight.
PYQ: 35 – CBSE 2025 – Code 30 – Series 5 – Set 1
Ans:
Step 1: Mean weight value of data:
To calculate the mean value, let’s re-organize the data:
To arrange the above, we take following steps:
- We calculate midpoint ‘x’ of each class by (lower value + higher value) / 2
- Then we calculate ‘fx’ by multiplying midpoint of each class with frequency of that class
- We calculate Σf by summing up all the frequencies and Σfx by adding up all the values of fx
Next, we know that, mean of grouped data is given by:
Mean of grouped data = Σfx / Σf = 1603 / 35 = 45.8
Hence, the mean value of the given data is 45.8 kg
Step 2: Median value of data:
To calculate the median value, let’s re-organize the data:
To find the median, we need to first identify middle class of the data.
- We know that, Median class is the class where the cumulative frequency crosses 50% of total of frequencies.
- Here, in the given data, total of frequencies is 35 and at row 5, cumulative frequency 28 is crossing 50% of total (i.e. 17.5)
- Hence, our Median class = 46 – 48
Next, the median value of a grouped data is given by:
Median = L+ [(n / 2 – F) / f ] x h
Here:
L = Lower boundary of the median class = 46
n = Total number of frequencies = 35
F = Cumulative frequency of the class before the median class = 14
f = Frequency of the median class = 14
h = Class width = 48 – 46 = 2
hence, the Median = L+ [(n / 2 – F) / f ] x h
= 46 + [(35 / 2 – 14) / 14] x 2
= 46 + [(17.5 – 14) / 14] x 2
= 46 + (3.5 / 14) x 2
= 46 + 7 / 14 = 46 + 0.5 = 46.5
Therefore, Median value of the grouped data is 46.5 kg
Step 3: Difference between mean and median weight :
Difference = ∣Mean−Median∣
= ∣(45.8−46.5)∣ = 0.7 kg
Therefore, difference between mean and median weight is 0.7 kg.
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