Question

The runs scored in a cricket match by 11 players is as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three the same?

Answer 1

Hint: First, we will the sum of the given runs scored in a cricket match and then divide the above value by 11 to find the value of mean. Then we will rearrange the series in ascending order and use formula to find the median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data. Then we will use that the mode is the most occurring observation of the data. Then compare the value to find if they are equal or not.

Complete step-by-step answer:
We are given runs scored in a cricket match by 11 players is as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Finding the sum of the given runs scored in a cricket match, we get
\[
   \Rightarrow 6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120 \\
   \Rightarrow 429 \\
 \]
Dividing the above value by 11 to find the value of mean, we get
\[
   \Rightarrow \dfrac{{429}}{{11}} \\
   \Rightarrow 39 \\
 \]
Thus, the mean is 39.
Rearranging the given series in ascending order, we get
6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
We know the formula to find the median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data.
After finding the number of observations, we have that \[n = 11\].
Substituting the value of \[n\] in the above formula, we get
\[
   \Rightarrow \dfrac{{11 + 1}}{2} \\
   \Rightarrow \dfrac{{12}}{2} \\
   \Rightarrow 6 \\
 \]
 So, we will take the 6th term from the terms in ascending orders, we have 15.
Thus, the value of median is 15.
We know that the mode is the most occurring observation of the data.
So using the given series, we get that 15 occurred the most times, that is, 3.
Hence, 15 is the value of mode.
No, the value of mean, median and mode are not the same.

Note: In solving these types of questions, students should know the formulae of mean, median and mode. The question is really simple, students should note down the values from the problem really carefully, else the answer can be wrong. One should take care while finding the mean, variance and avoid calculation mistakes.