Question

Weight of 40 eggs were recorded as given below:

Weight(in gms)	85 - 89	90 - 94	95 – 99	100 – 104	105 - 109
Number of eggs	10	12	12	4	2

The lower limit of the median class is
(a) 90
(b) 95
(c) 94.5
(d) 89.5

Answer 1

Hint:We will first find the cumulative frequency and then we will find the median class. We will divide the sum of frequencies by 2 to get the median class and finally we will find the lower limit of the median class.

Complete step-by-step answer:
It is given in the question that we have 40 eggs and the weights of the eggs are distributed in different categories as

Weight(in gms)	85 - 89	90 - 94	95 – 99	100 – 104	105 - 109
Number of eggs	10	12	12	4	2

We are also given a total number of eggs as 40. So, sum of frequency $\sum{{{f}_{i}}=40}$. Now, we will find cumulative frequency.
Basically cumulative frequency means the total of a frequency and all the frequency so far in a frequency distribution we can also say it as running total frequency. For example, we can find the cumulative frequency by adding 10 to 12 and we get 22, then we will add 22 to 12 and then we will get 34 and so on. So, we can represent it in tabular form as below

Weight (in gms)	Number of eggs (frequency)	Cumulative frequency
85 – 89	10	10
90 – 94	12	22
95 – 99	12	34
100 – 104	4	38
105 - 109	2	40
	40

Now, we have the sum of frequency, $\sum{{{f}_{i}}=40}$. So, the median class will be that class whose cumulative frequency will be next to $\dfrac{N}{2}=\dfrac{40}{2}=20$. The number just greater than 20 is 22 and thus the class is 90 – 94. It means the median class is 90 – 94 therefore the lower limit is 90.
Thus, option a) is the correct answer.

Note: Usually students make mistakes in writing cumulative frequency. It is noted that the last cumulative frequency is always equal to the sum of frequency. In this question, we have the last cumulative frequency as 40, which is equal to the sum of frequency. So, we have distributed and put all the values correctly. If they do not match this means that we may have made some mistake in addition or in copying the values from the question. It is recommended to do the cumulative frequency part in this question carefully.