Understanding Mean and Median Calculations

The question asks us to find the mean and the median for a given set of heights of 5 students. The heights are 150 cm, 165 cm, 161 cm, 144 cm, and 155 cm.

Let's calculate each measure of central tendency step-by-step.

Calculating the Mean Height

The mean (or average) is calculated by summing all the values in a dataset and then dividing by the total number of values. The formula for the mean is:

\(\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}\)

In this case, the values are the heights of the 5 students:

• Sum of heights = \(150 + 165 + 161 + 144 + 155\)
• Sum of heights = \(775\) cm
• Number of students = \(5\)

Now, we calculate the mean:

\(\text{Mean} = \frac{775}{5}\)

\(\text{Mean} = 155\) cm

So, the mean height of the students is 155 cm.

Calculating the Median Height

The median is the middle value in a dataset that is arranged in ascending or descending order. When the number of observations (n) is odd, the median is the \(\left(\frac{n+1}{2}\right)^{\text{th}}\) observation after arranging the data.

First, let's arrange the given heights in ascending order:

144, 150, 155, 161, 165

The number of observations is n = 5, which is an odd number.

The position of the median is \(\left(\frac{5+1}{2}\right)^{\text{th}}\) = \(\left(\frac{6}{2}\right)^{\text{th}}\) = \(3^{\text{rd}}\) position.

Looking at the sorted list, the value at the 3rd position is 155.

Sorted heights: 144, 150, 155, 161, 165

So, the median height of the students is 155 cm.

Summary of Results

Based on our calculations:

• Mean height = 155 cm
• Median height = 155 cm

The values of mean and median respectively are 155 and 155.

Revision Table: Key Statistics Concepts

Here is a quick look at the measures of central tendency discussed:

Additional Information on Calculating Median

The method for calculating the median depends on whether the number of data points (n) is odd or even.

• If n is odd: Arrange the data in order and the median is the value at the \(\left(\frac{n+1}{2}\right)^{\text{th}}\) position.
• If n is even: Arrange the data in order and the median is the average of the values at the \(\left(\frac{n}{2}\right)^{\text{th}}\) and \(\left(\frac{n}{2}+1\right)^{\text{th}}\) positions.

In this specific problem, n=5 (odd), so the median is the value at the \(\left(\frac{5+1}{2}\right)^{\text{th}}\) = 3rd position in the sorted list.