Question

Here are two datasets:

Dataset A: 64 65 66 68 70 71 72
Dataset B: 64 65 66 68 70 71 720

For dataset A, the mean and median are 68. Looking at dataset B, notice that all of the observations except the last one are close together. Which measure will be affected by this last observation in dataset B?

a. Mean
b. Median

Answer 1

Answer:

Option a) Mean

Mean is affected a lot by the change in the last observation as the median remains the same.

Step-by-step explanation:

we are given the following in the question:

Data set A: 64, 65, 66, 68, 70, 71, 72

Data set B: 64, 65, 66, 68, 70, 71, 720

For data set A, the mean and median are 68.

For data set B:

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1124}{7} = 160.57$

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data:

64, 65, 66, 68, 70, 71, 720

$\text{Median} = \dfrac{7+1}{2}^{th} \text{ term} = 4^th\text{ term} = 68$

Clearly, 720 is the is a outlier.

As seen mean is affected a lot by the change in the last observation as the median remains the same.

Answer 2

The measure that will be affected by this last observation in dataset B is mean

Given:

Dataset A: 64 65 66 68 70 71 72

Dataset B: 64 65 66 68 70 71 720

• The mean and median of dataset A are 68

How to find mean and median

Mean of dataset B = (64 + 65 + 66 + 68 + 70 + 71 + 720) / 7

= 1,124 /7

= 160.571428571428

• Median = 68

Therefore, measure that will be affected by this last observation in dataset B is mean

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