Unit 5: Measures of Central Tendency

Question 1

Measures of Central Tendency

Answer 1

Mode
* Median
* Mean

Question 2

Mode

Answer 2

The most frequently occurring value in a group.

Mode can be a bad measure of central tendency when there are not many
data points

Question 3

Unimodal

Answer 3

• Unimodal: data has one mode
• Example: number of school absences: 0 0 0 2 3 5
• Mode is 0

Question 4

Bimodal

Answer 4

• Bimodal: data has two modes
• Example: number of school absences: 0 0 0 2 3 3 3 5
• Two modes 0 and 3.

Question 5

Median

Answer 5

The median Mdn or 𝑥෥ is the midpoint of a distribution
* Half of the observations are smaller and the other half are larger

Question 6

• How to find median:

Answer 6

1. Arrange all observations from smallest to largest.
2. If n is odd, the median Mdn is the center observation in the ordered list.
3. If n is even, the median Mdn is the average of the two center observations in the
   ordered list.

Question 7

Mean

Answer 7

Mean M (average) of n observations:

Question 8

What happens to the median and mean when
the data is skewed to the right?

Answer 8

when the distribution of data is skewed to the left, the mean is often less than the median. When the distribution is skewed to the right, the mean is often greater than the median. In symmetric distributions, we expect the mean and median to be approximately equal in value

Question 9

The Effect of Outliers

Answer 9

An outlier is a value or score in a group that is much higher or lower
than the other values in the group.
* For example: add a score of 0
93 92 88 90 0
* Mean change from 90.75 to 72.6
* The median nearly unaffected ( 0 88 90 92 93)
* Median less affected by outliers than mean

Question 10

why is median often used as the
measure of central tendency

Answer 10

The median is less affected by outliers and skewed data than the mean and is usually the preferred measure of central tendency when the distribution is not symmetrical.