Question

12, 9, 15, 19, 20, 15 Mean Median Mode

Answer 1

Answer:

Mean: 15

Median:  15

Mode:  15

Step-by-step explanation:

Definitions:

Mean: It represents the average value of a given data set. The formula for finding the mean of a given set of numbers by taking the quotient of all numbers and the number of values. In other words:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

Median: It represents the middle value in a given set of numbers. In order to determine the median, it is essential to arrange the given data either in ascending or descending order (although it is customary to arrange the numbers into ascending order).

• If there is an odd number of values in a given set, then the middle number is the median of that set.

• If a given list comprises of an even number of items, then we must take the average of the two middle numbers.

Mode: It represents the number that occurs most often on a list of items or data.

Solution:

Find the Mean:

Using the formula provided in the previous section for finding the mean:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

$\displaystyle\mathsf{Mean\:=\:\frac{12+9+15+19+20+15}{6}\:=\:\frac{90}{6}\:=\:15}$

Find the Median:

Arrange the given data set in ascending order:

12, 9, 15, 19, 20, 15  ⇒  9, 12, 15, 15, 19, 20

Next, since there is an even number of items on our given data set, we must take the average of the two middle numbers (which are 15 and 15):

$\displaystyle\mathsf{Median\:=\:\frac{15+15}{2}\:=\:\frac{30}{2}\:=\:15}$

Therefore, the median is 15.

Find the Mode:

As described in the previous section of this post, the mode is the number that occurs most often on our given data. The only repeating number on our list is 15, hence it is the mode.

Therefore, the mean, median, and mode of the given data set is 15.