Question

Weight of 40 eggs were recorded as given below

Weight in grams	Number of eggs
85-90	4
90-94	12
95-99	14
100-104	8
105-109	2

Find the modal weight.

Answer 1

Hint: Mode is the value with highest frequency or highest repeating value. Mode of grouped frequency data is given by the formula $Mode = l + \left( {\dfrac{{{f_m} - {f_1}}}{{2{f_m} - {f_1} - {f_2}}}} \right) \times h$, where ${f_m}$ is the frequency of the modal class, ${f_1}$ is the frequency of the class which is above modal class, ${f_2}$ is the frequency of the class which is below the modal class, h is the length of the class and l is the lower limit of the modal class.

Complete step-by-step answer:
We are given a frequency distribution of weight of 40 eggs.
We have to calculate the modal weight of this recorded data.
From the data, the highest frequency ${f_m}$ is 14.
The class with the highest frequency (14) is called the modal class, which is 95-99.
The lower boundary of the modal class l= 95.
The frequency ${f_1}$ of the class which is previous to the modal class is 12.
The frequency ${f_2}$ of the class which is next to the modal class is 8.
The height of the class interval of the given data is 5.
$
  Model + \left( {\dfrac{{{f_m} - {f_1}}}{{2{f_m} - {f_1} - {f_2}}}} \right) \times h \\
  l = 95,h = 5,{f_m} = 14,{f_1} = 12,{f_2} = 8 \\
  Mode = 95 + \left( {\dfrac{{14 - 12}}{{\left( {2 \times 14} \right) - 12 - 8}}} \right) \times 5 \\
  \to Mode = 95 + \left( {\dfrac{2}{{28 - 20}}} \right) \times 5 \\
  \to Mode = 95 + \left( {\dfrac{{10}}{8}} \right) \\
  \to Mode = 95 + 1.25 \\
 \therefore Mode = 96.25grams \\
$
The modal weight is 96.25 grams.

Note: The mode of a given data is simply the most common or repeating value. There can be more than one mode in a given data. We talk about modal class in the grouped data, because the individual values of the data are not given in grouped data.
 Mean is the average value of the given data. Median is the middle value in the given data. A given data can have more than one mode values but only one mean value and one median value. Do remember this point.