Question

Find the mean of $28,24,37,42,56,59,67,28,15,$and $32$
A) $38.8$
B) $60$
C) $70$
D) None of these

Answer 1

Hint: According to given in the question we have to determine the mean of the given data $28,24,37,42,56,59,67,28,15,$ and $32$ so, first of all we have to understand of the mean which is explained below:
Mean: The mean is basically a way to find the average of the given data but before that we have to arrange the all data or given number into ascending order means we have to arrange all the given data from the smaller number to the largest number and after that we have to add up all the given data or number and same as we have to determine the total number of given data or terms. And after that we have to use the formula to find the mean as given below:

Formula used: Mean $(\overline x ) = \dfrac{{\sum\limits_{i = 1}^{i = n} {{x_i}} }}{n}.......................(a)$
Where, n is the total number of terms. Hence, on substituting all the values in the formula above we can obtain the mean for the given data.

Complete step-by-step solution:
Step 1: First of all we have to arrange all the numbers $28,24,37,42,56,59,67,28,15,$ and $32$ in ascending order. Hence,
Data in ascending order: $15,24,28,28,32,37,42,56,59,67$
Step 2: Now, we have to add all the terms in ascending order as obtained in step 1. Hence,
Sum of terms:
$
   \Rightarrow \sum\limits_{i = 1}^{i = 10} {{x_i} = 15 + 24 + 28 + 28 + 32 + 37 + 42 + 56 + 59 + 67} \\
   \Rightarrow \sum\limits_{i = 1}^{i = 10} {{x_i} = 388}
 $
Step 3: Now, we have to obtain the total number of terms in the given data. Hence,
$ \Rightarrow n = 10$
Step 4: Now, we have to use the formula (a) as mentioned in the solution hint to find the mean for the given data. Hence, on substituting all the values,
$
  \overline x = \dfrac{{388}}{{10}} \\
  \overline x = 38.8
 $
Hence, with the help of formula (a) we have obtain the mean for the given data $28,24,37,42,56,59,67,28,15,$ and $32$ which is $\overline x = 38.8$

Option A is the correct answer.

Note: Mean can be determined by arranging the given data in ascending order and then we have to divide the sum of all the given data with the total number of given data.
The mean of the absolute values of the numerical differences between the numbers of a set such as, a static data and their mean and median.