Descriptive Statistics

Question 1

Define measures of central tendency?

Answer 1

These inform us about the centre of the data

Question 2

What are the 3 measures of central tendency?

Answer 2

Mean, median, mode

Question 3

How do you calculate the mean?

Answer 3

Question 4

What are the advantages of using the mean?

Answer 4

It is a ver sensitive statistic because it takes into account the exact value of all the data
It is representative of all of the data

Question 5

What are the disadvantages of using the mean?

Answer 5

If one of extremely high or low (an anomaly) then the mean can be distorted and therefore misrepresent the data
It can be used with nominal data

Question 6

How do you calculate the median?

Answer 6

The middle value in an ordered list. All data must be ordered numerically in a list. If there is an even number of data then you get the 2 central items add them and then divide by 2 to get the median

Question 7

What are the advantages of using the median?

Answer 7

It isn’t effected by extreme scores so it can be useful under such circumstances
It is easy to calculate
It isn’t distorted by any anomalies

Question 8

What are the disadvantages of using the median?

Answer 8

It doesn’t reflect the whole data set
It is less sensitive than the mean because exact values may not always be used

Question 9

How do you calculate then mode?

Answer 9

The most frequent value
You can have data sets with bi or tri modal data sets

Question 10

What are the advantages of using the mode?

Answer 10

It is unaffected by anomalies
It is useful for discrete data
The only measure of central tendency that can be used for nominal data
It’s output is a piece of data, you can’t have 2.4 children

Question 11

What are then disadvantages of using the mode?

Answer 11

Sometimes there maybe too many modes that using it becomes meaningless
It doesn’t represent the full data set

Question 12

Define measures of dispersion?

Answer 12

A type of descriptive statistic that finds out how spread out the data items are

Question 13

What are the 2 measures of dispersion?

Answer 13

Range
Standard deviation

Question 14

Define the range?

Answer 14

the arithmetic distance between the top and the bottom values in a set of data

Question 15

What are the advantages of using the range?

Answer 15

It is easy to calculate
Even if 2 sets of data have the same mean they could have different ranges so the range can be used well to describe the data

Question 16

What are the disadvantages of using the range?

Answer 16

It is effected by extreme values
If fails to take into account the distribution of the numbers (eg 1,2,72)
Could use IQR

Question 17

Define standard deviation?

Answer 17

The standard deviation is a more precise way of measuring the spread of the data. It is the measure o9f the average distance between each data item and the mean (ignoring plus and minus values)

Question 18

What does a small standard deviation mean?

Answer 18

The data set is quite compact

Question 19

What are the advantages of using the standard deviation?

Answer 19

Precise measure of dispersion because it takes into account all values

Question 20

What are the disadvantages of standard deviation?

Answer 20

It may hide some of the characteristics of the data set eg extreme values

Question 21

Why do you add 1 onto the range?

Answer 21

To avoid rounding errors