Measures of Central Tendancy

Question 1

What are the 3 measures of central tendency?

Answer 1

1. Mode
2. Mean
3. Median

Question 2

What does bimodal mean?

Answer 2

A data set in which 2 modes can be identified

Question 3

What does multi modal mean?

Answer 3

A data set in which two or more modes can be identified

Question 4

What is the mode?

Answer 4

The data value that occurs most frequently in the set

Question 5

How is mode calculated?

Answer 5

Put the raw data in order so that values which are the same will appear together in the list

Question 6

What is frequency distribution?

Answer 6

A table that shows the frequency with which each value occurs in a data set

Question 7

What is grouped frequency distribution?

Answer 7

A table in which the values are formed into groups and the number of occurrences in each group from a data set is recorded.

Question 8

Which data type is more appropriate for using the mode?

Answer 8

The mode is a suitable measure of central tendency when the data are QUALITATIVE Mode can be used for quantitative data as well but it is not very informative when a data set is multimodal or has no mode at all

Question 9

What is mean?

Answer 9

The average of all the data in the set

Question 10

How do you calculate the mean?

Answer 10

Sum of data values / No. values in the set

Question 11

What is the equation of the mean for a raw data set?

Answer 11

Question 12

What is the equation for the mean if the data is summarised in a grouped frequency distribution?

Answer 12

Question 13

How do you work out the mean when the data is summarised in a grouped frequency distribution?

Answer 13

Use the frequency distribution formula where each value of x is represented by the class mid-point

Question 14

What type of data is the mean suitable for?

Answer 14

Discrete or continuous quantitative data

It is not suitable for qualitative data set which does not contain numerical values

Question 15

Why is the mean the most popular measure of central tendancy?

Answer 15

The calculation uses all of the data values and is therefore truly representative of the whole set

Question 16

What is the problem with using the mean?

Answer 16

It can be highly influenced by extreme values

Question 17

What is the median?

Answer 17

The middle point when the data set is ordered

The middle value which divides a set of ordered data into 2 halves

Question 18

How is the median found when n is an odd number and a single middle value exists (raw data and frequency distribution)?

Answer 18

1/2(n+1)

Question 19

How is the median found when n is an even number (raw data and frequency distribution)?

Answer 19

Identify the two values closest to the middle and find their average

Their positions found in an ordered set of data are found using : 1/2n and 1/2n+1

E.g. there are 6 customers in the queue for till 14, so the position of the two values closest to the middle are found usinfg 1/2(6) and 1/2(6)+1 which identifies the amount of money spent by the 3rd and 4th customers

Question 20

What formula do we apply when trying to find the median for grouped frequency distribution?

Answer 20

• b = lower case boundary
• f = the sum of all frequencies that occur before the median class
• fm = the frequency of the median class
• w = the class width of the median class

Question 21

What are the advantages of using mode?

Answer 21

• Always easy to understand and calculate
• Can be used for both quantitative and qualitative data
• Unaffected by extreme values
• Always is one of the data values in the set

Question 22

What are the advantages of using mean?

Answer 22

• Mostly easy to understand and calculate
• Uses all of the data values in the set
• Provides a single response

Question 23

What are the advantages of using median?

Answer 23

• Provides a single result
• Is sometimes one of the data values in the set