Find the mean and compare it with the median. Find the standard deviation and compare it with the interquartile range

Question:

Find the mean and compare it with the median. Find the standard deviation and compare it with the interquartile range. Calculate s for the data 4, 1, 3, 10, 2.

(a)

(b)

Step-by-step explanation:

Given:

Data: 4, 1, 3, 10, 2.

Solving (a): The mean and the Median

The mean is calculated as follows:

Where

i.e 5 data

So, the expression becomes:

Calculating the Median:

First, arrange the order (ascending order):

Because n is odd

The median is represented as:

From the arranged data, the 3rd item is 3.

Hence:

By comparison, the mean is greater than the median because

Solving (b): Standard Deviation and IQR

The standard deviation is calculated as follows:

So, we have:

Calculating IQR

In (a), we calculate the median as:

First, we calculate

The first half is:

So:

First, we calculate

So:

Recall that:

So, we have:

By comparison, the standard deviation is greater than the IQR because:

So,