Question

Find the mode, and the mean for the set of data below.
Number of fiction books read by 28 eight-grade pupils:
4, 6, 1, 7, 3, 9, 5, 7, 8, 5, 4, 6, 10, 6, 9, 5, 6, 6, 8, 6, 8, 5, 10, 7, 2, 5, 3, 7.​

Answer 1

Hint: Here we will find the number with highest frequency to find the mode of the given data and we will find the average of all the terms in order to get the value of mean.
The mean is given by:-
\[mean = \dfrac{{{\text{sum of all terms}}}}{{{\text{number of terms}}}}\]

Complete step-by-step answer:
The given data is:-
4, 6, 1, 7, 3, 9, 5, 7, 8, 5, 4, 6, 10, 6, 9, 5, 6, 6, 8, 6, 8, 5, 10, 7, 2, 5, 3, 7.​
Now in order to find the mode of he given data we need to find the number which has occurred
maximum number of times.
So we will observe the occurrence of each of the numbers in the given data.
4 has occurred 2 times.
6 has occurred 6 times
1 has occurred 1 time
7 has occurred 4 times
3 has occurred 2 times
9 has occurred 2 times
5 has occurred 5 times
8 has occurred 3 times
10 has occurred 2 times
2 has occurred 1 time
So we can see that 6 has occurred the most number of times
Hence 6 is the mode of the given data.
Now we will calculate the mean of the above data:-
We know that the mean of a data is given by:-
\[mean = \dfrac{{{\text{sum of all terms}}}}{{{\text{number of terms}}}}\]
Here the number of terms are 28
Hence applying this formula we get:-
\[mean = \dfrac{{4 + 6 + 1 + 7 + 3 + 9 + 5 + 7 + 8 + 5 + 4 + 6 + 10 + 6 + 9 + 5 + 6 + 6 + 8 + 6 + 8 + 5 + 10 + 7
+ 2 + 5 + 3 + 7}}{{28}}\]
Simplifying it we get:-
\[mean = \dfrac{{168}}{{28}}\]
On dividing we get:-
\[mean = 6\]

Hence the mean is 6 and mode is also 6.

Note: Students should take note that mode is the value which occurs most frequently in a set of observations and it is called the point of maximum frequency.
Also, each term should be counted carefully and should be cross checked also in order to avoid mistakes in answers.