1.3 Measures of Central Tendency for Sample Data

Question 1

How many centers can there be for the same sample of data in statistics?

Answer 1

Up to three centers for the same sample of data

Question 2

What is the “three m statistics”?

Answer 2

• Mode - Median - Mean

Question 3

When would a sample mode exist?

Answer 3

For any type of sample data (qualitative or quantitative)

Question 4

When would a sample median exist?

Answer 4

• May exist for a qualitative sample data - Always exists for quantitative sample data

Question 5

When would a sample mean exist?

Answer 5

Restricted to quantitative sample data

Question 6

When do the three centers coincide? What are the two conditions?

Answer 6

1) The sample distribution is symmetrical 2) It has one and only one mode (unimodal)

Question 7

What is the mode?

Answer 7

The most frequent value in the sample

Question 8

What is the median?

Answer 8

• The middle number - Found by ordering all data points and picking out the one in the middle - Or, if there are two middle numbers, taking the mean of those two numbers).

Question 9

For continuous quantitative data, how may the mode be reported?

Answer 9

• The interval (e.g. 80-90) - The midpoint (e.g. 85)

Question 10

What must be done to quantitative data to derive the mean?

Answer 10

• The quantitative data must be ranked first - Raw data cannot be used

Question 11

What is the median for quantitative data when n is an odd number?

Answer 11

The median represents the middle value after determining the ranked quantitative data

Question 12

What is the median for quantitative data when n is an even number?

Answer 12

The median represents the average of the two middle values after determining the ranked quantitative data

Question 13

What is the sample median for qualitative data when n is an odd number?

Answer 13

The median represents the middle value after determining the ranked qualitative data

Question 14

What is the sample median for qualitative data when n is an even number?

Answer 14

• The sample median does not exist if the two middle values are different, as an average may not be determined - The sample median does exist if the two middle values are the same, as an average may be determined

Question 15

What is the sample median for qualitative data when n is an even number?

Answer 15

• The sample median does not exist if the two middle values are different, as an average may not be determined - The sample median does exist if the two middle values are the same, as an average may be determined

Question 16

Must quantitative data be ranked to calculate the mean?

Answer 16

No, there is no need to rank the data

Question 17

Why can’t a sample mean be calculated for qualitative data?

Answer 17

Because qualitative data is not divisible

Question 18

How can we quantify information with qualitative data?

Answer 18

Frequency data may be qualitative or quantitative, but the frequency is always quantitative

Question 19

What measure should be used if there are multiple outliers?

Answer 19

The median

Question 20

What is the equation for the mean?

Answer 20

Question 21

What is the equation for the weighted mean?

Answer 21