RM - Measures of central tendency and dispersion

Question 1

What do descriptive statistics do?

Answer 1

Identify general patterns and trends.

Question 2

What are the 4 levels of measurement?

Answer 2

Nominal
Ordinal
Interval
Ratio

NOIR

Question 3

What is nominal data?

Answer 3

Data is in separate categories.

Question 4

What is ordinal data?

Answer 4

Data is ordered in some way. The ‘difference’ between each item is not the same.

Question 5

What is interval data?

Answer 5

Data is measured using units of equal intervals.

Question 6

What is ratio data?

Answer 6

There is a true zero point as in most measures of physical quantities.

Question 7

What level of measurement is it when data is in separate categories?

Answer 7

Nominal

Question 8

What level of measurement is it when data is ordered in some way and the ‘difference’ between each item is not the same?

Answer 8

Ordinal

Question 9

What level of measurement is it when data is measured using units of equal intervals?

Answer 9

Interval

Question 10

What level of measurement is it when there is a true zero point as in most measures of physical quantities?

Answer 10

Ratio

Question 11

What do measures of central tendency do?

Answer 11

Inform us about central (or middle) values for a set of data. They are ways of calculating a typical value for a set of data.

Question 12

What are the 3 measures of central tendency?

Answer 12

Mean
Median
Mode

Question 13

How is mean calculated?

Answer 13

By adding up all the data items and dividing by the number of data items.

Question 14

What levels of data can the mean be used with?

Answer 14

Ratio and interval only.

Question 15

How is the median calculated?

Answer 15

All data items must be arranged in order and then the central value is the median. If there is an even number of data items and therefore two middle values, add the two middle values and divide by two.

Question 16

What levels of data can the median be used with?

Answer 16

Ratio, interval and ordinal data only.

Question 17

How is mode calculated?

Answer 17

Nominal - category that has the highest frequency count.

Interval and ordinal - the data item that occurs most frequently.

Question 18

What is it called when a set of data has 2 modes?

Answer 18

Bi-modal.

Question 19

What are the 2 measures of dispersion?

Answer 19

Range

Standard deviation

Question 20

Why is there an addition of 1 when calculating the range of a set of data?

Answer 20

Because the bottom number could represent a value as low as 0.5 lower than the bottom number and the top number could represent a number of up to 0.5 higher than what it is (due to rounding etc).

Question 21

What is the most precise method of expressing dispersion?

Answer 21

Standard deviation

Question 22

What is standard deviation a measure of?

Answer 22

Dispersion but more precisely, a measure of the average distance between each data item above and below the mean, ignoring plus or minus values.

Question 23

What are the strengths of using the mean?

Answer 23

It is the most sensitive measure of central tendency because it takes account of the exact distance between all the values of all the data.

Question 24

What are the limitations of using the mean?

Answer 24

Its sensitivity means that it can easily be distorted by one (or a few) extreme values and thus end up being misinterpretive of the data as a whole.

Cannot be used with nominal data.

Doesn’t make sense to use it when you have discrete values such as average number of legs.

Therefore the mean isn’t always representative of the data as a whole and should always be considered alongside the standard deviation.

Question 25

What are the strengths of using the median?

Answer 25

Not affected by extreme scores. Appropriate for ordinal (ranked) data. Can be easier to calculate than the mean. Therefore, it can be used to describe a variety of data sets, including skewed data and non-normal distributions.

Question 26

What are the limitations of using the median?

Answer 26

Not as 'sensitive' as the mean because the exact values are not reflected in the final calculation.

Question 27

What are the strengths of using the mode?

Answer 27

Unaffected by extreme values. Much more useful for discrete data. The only method that can be used when the data are in categories - nominal data.

Question 28

What are the limitations of using the mode?

Answer 28

Not a useful way of describing data when there are several modes. Tells us nothing about the other values in a distribution. Therefore, the key is to use the mode only with data sets for which it is appropriate.

Question 29

What are the strengths of using the range?

Answer 29

Easy to calculate. Useful for ordinal data or with highly skewed data or when making a quick calculation.

Question 30

What are the limitations of using the range?

Answer 30

Affected by extreme values. Fails to take account of the distribution of the numbers - for example, it doesn't indicate whether most numbers are closely grouped around the mean or spread out easily.

Question 31

What are the strengths of using standard deviation?

Answer 31

A precise measure of dispersion as takes all the exact values into account. Not difficult to calculate if you have a calculator.

Question 32

What are the limitations of using standard deviation?

Answer 32

May hide some of the characteristics of the data set (e.g. extreme values). Therefore, best used together with the mean to describe interval or ratio data which is normally distributed.

Question 33

Define mean:

Answer 33

The arithmetic average of a data set. Takes the exact values of all the data into account.

Question 34

Define measure of central tendency:

Answer 34

A descriptive statistic that provides information about a 'typical' value for a set of data.

Question 35

Define measure of dispersion:

Answer 35

A descriptive statistic that provides information about how spread out a set of data are.

Question 36

Define median:

Answer 36

The middle value of a data set when the items are placed in rank order.

Question 37

Define mode:

Answer 37

The most frequently occuring value or item in a data set.

Question 38

Define range:

Answer 38

The difference between the highest and lowest item in a data set. Usually one is added as a correction.

Question 39

What does standard deviation do?

Answer 39

Shows the amount of variation in a data set. It assess the spread of data around the mean.