Q11. - Algebra 1

Question

Which measure of central tendency best represents the data? Justify your answer. Then find the measure. 

The cafeteria wants to show the best representation of how much students spend on lunch: 2, 3, 4, 3, 2, 4, 1, 3, 4, 2, 3, 3, 4, 3.

Step-by-Step Solution

Answer

The best measure of central tendency to represent the data is median of the data and the value of median is 3.

Step 1. Define the measure of central tendency.

A measure of central tendency is a summary statistic that represents the center point or typical value of a datasheet.

The 3 most common measures of central tendency are the mean, median and mode.

Step 2. Define median.

The median is the middle number in a sorted, ascending or descending, list of numbers.

 Median $={\left(\frac{n+1}{2}\right)}^{\text{th}}$ term, if the number of values in data sheet $\left(n\right)$ is odd.

Median $=\frac{{\left(\frac{n}{2}\right)}^{\text{th}}\text{term}+{\left(\frac{n}{2}+1\right)}^{\text{th}}\text{term}}{2}$, if the number of values in data sheet $\left(n\right)$ is even.

Step 3. Calculate the measure of central tendency that best represents the given data.

The amount to spend on lunch by the students are: 

2, 3, 4, 3, 2, 4, 1, 3, 4, 2, 3, 3, 4, 3 

List the data in ascending order.

1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4

Observe the data.

There are some values which are repeating and also there is not a big gap in the middle of the data.

So, median would best represent the data.

The number of data values $\left(n\right)=14$ (even)

Hence, 

Median $=\frac{{\left(\frac{n}{2}\right)}^{\text{th}}\text{term}+{\left(\frac{n}{2}+1\right)}^{\text{th}}\text{term}}{2}$ 

Substitute $n=14$.

Median $=\frac{{\left(\frac{14}{2}\right)}^{\text{th}}\text{term}+{\left(\frac{14}{2}+1\right)}^{\text{th}}\text{term}}{2}$

Median $=\frac{7^{\text{th}}\text{term}+8^{\text{th}}\text{term}}{2}$

Median $=\frac{3+3}{2}$

Median $=\frac{6}{2}$

Median $=3$

 

Therefore, the best measure of central tendency to represent the data is median of the data and the value of median is 3.