Question

What are the measures of central tendency for the data set $5,5,10,10,5,20,25$?

Answer 1

Hint: First, we need to know about the concept of the measures of central tendency. Which is nothing but the statistical approach to find the mean, median, and mode of the given data. Where mean is all about the average of the given data, the median is the middle value of the given data, and mode is the most or frequency repeated value in the given data.

Complete step by step answer:
As we know the measure of central tendency is the mean, median, and mode of the given data.
So, let us solve the mean of the data $5,5,10,10,5,20,25$
The mean formula is $M = \dfrac{{\sum X }}{n}$ summation is the sum or addition of given data and n-is the total numbers.
Hence, we get $M = \dfrac{{5 + 5 + 10 + 10 + 5 + 20 + 25}}{7}$
Further solving we get $M = \dfrac{{80}}{7} = 11.4$ is the mean of the given data.
The median of the given data $5,5,10,10,5,20,25$ is $10$ because there are a total of seven numbers and $10$ is the middle number. We also check the median as $5,5,5,10,10,20,25$ change into ascending and also the median is $10$ the middle value.
The mode of the given data of $5,5,10,10,5,20,25$ is $5$ because $5$ is the highest repeated of $3$
Hence the mean is $11.4$ and the median is $10$ and mode is $5$

Note:
Once we found the given problem is all about the mean, median, and mode. Then it was easy to solve according to the given formulas and methods.
Which are the measures of central tragedy being nothing but the mean, median, mode of the given data.
Also, for the median, if the given entries' numbers count is odd, then the middle value is the median of the given data.