Measures of Central Tendency

Question 1

Why is it important to summarise data?

Answer 1

Data can be very complex and there can be lots of it so it’s useful to be able to summarise it

Question 2

What is a measure of central tendency?

Answer 2

A measurement which should provide an indication of a “typical” score in the data set (usually in the middle but not always)

Question 3

What are the 3 common measures of central tendency?

Answer 3

1) Mean
2) Median
3) Mode

Question 4

How do you calculate the mean?

Answer 4

• Add all the data together
• Divide the total/sum but the number of scores

Question 5

What of the pros and cons of using the mean as the main measure of central tendency?

Answer 5

Pro = Provides an estimate of the average score in the data set (reasonable representation of score)

Con = Is affected by extreme outlier data points (can be misleading)

Question 6

What are the pros and cons of using the median as the main measure of central tendency?

Answer 6

Pro = Is insensitive to extreme scores in the data set

Con = Doesn’t reflect the shape of the scores – i.e. doesn’t care how far away extreme scores are (does not use all info available in the data set)

Question 7

What of the pros and cons of using the mode as the main measure of central tendency?

Answer 7

Pro = Easy to calculate from a histogram and easy to understand (the most common value)

Con = Data set might have more than 1 mode or no mode at all

Question 8

How do you calculate the median?

Answer 8

• Arrange/rank data in ascending order
• Find the midpoint

Question 9

How do you calculate the mode?

Answer 9

• Either plot the data on a graph or arrange/rank the data in ascending order
• Find the data which appears the most/most frequently occurring data

Question 10

When will the mean, the median and the mode all be the same?

Answer 10

When the distribution is symmetric

e.g. data set = 4, 3, 4, 3, 4, 6, 4

Mean = 4
Median = 4
Mode = 4

Question 11

Which measure of central tendency should you use here?

1, 1, 1, 2, 2, 3, 4, 5, 5, 6

Answer 11

Mean

• There’s no extreme values and you can find a reliable average value

Question 12

Which measure of central tendency should you use here?

1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 50

Answer 12

Mode

• Because there’s only 1 mode
• You cannot use mean because 50 is an extreme value which may pull up the average

Question 13

Which measure of central tendency should you use here?

1, 27, 28, 29, 30

Answer 13

Median

• Because 1 is an extreme value that may pull down the average
• The rest of the data seem close together in variability so median would be best