Question

How do you find the mean and median of the data set: There are $28,30,29,26,31\,and\,30$ students in a school’s six Algebra I classes?

Answer 1

Hint: In this question, we will find the mean by adding all the numbers and then dividing the sum by the total number of terms. To find the median first we will check whether the number of terms in the set is even or odd. If it is odd, then the middle term is the median, if it is even then the median is the average of the middle most two terms.

Complete step-by-step answer:
In the above question, first we will find the mean of given data using the formula of mean.
To find the mean of a data set you have to add all the values and divide the sum by the number of data:
$Mean = \dfrac{{\sum {{x_i}} }}{n}$
$ \Rightarrow Mean = \dfrac{{{x_1} + {x_2} + {x_3} + ... + {x_n}}}{n}$
$ \Rightarrow Mean = \dfrac{{28 + 30 + 29 + 26 + 31 + 30}}{6}$
$ \Rightarrow Mean = \dfrac{{174}}{6} = 29$
Now,
we will find the median of given set of data.
For that first we will arrange the given set of data in the ascending order.
Therefore,
 The given set of data is \[26,28,29,30,30,31\].
Now you have to look for the middle term in the ordered set.
If the number of all data is odd, then there is only one such number, else there are two such numbers.

In first case it is the middle term of the ordered set or we can use the formula, $Term = \dfrac{{n + 1}}{2}$
to find the term of the given set.
In the second case to calculate the median we have to find the mean of middle $2$ numbers or we can use the formula $Term = \dfrac{n}{2},\,\dfrac{n}{2} + 1$ and then we will find the mean of these two terms.
This set has $6$ elements, so there are $2$ middle numbers from the given set of data \[26,28,29,30,30,31\] as $29\,and\,30$.
Therefore, now we will find the mean of $29\,and\,30$ to find the median.
$Median = \dfrac{{29 + 30}}{2}$
$Median = \dfrac{{59}}{2} = 29.5$
Therefore, the mean of the given set of data is $29$ and the median is $29.5$.

Note: Mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by the number of observations in the data set. The median is the middle number in a data set when the numbers are listed in either ascending or descending order. The mode is the value that occurs the most often in a data set and the range is the difference between the highest and lowest values in a data set.