Measures of central tendency + dispersion

Question 1

What are the measures of central tendency?

Answer 1

The measures of central tendency are ‘averages’ which give us information about the most typical values in a set of data

Question 2

How many types of measures of central tendency do you need to consider?

What are the names of the different measures of central tendency?

Answer 2

There are three types of measures of central tendency to consider;

1. Mean
2. Median
3. Mode

Question 3

What is the mean?

Answer 3

The mean is the average

Question 4

How is the mean calculated?

Answer 4

The mean is calculated by adding up al. the score or values in a set of data and dividing this figure by the total numbers of scores there are

Question 5

Work out the mean of these numbers:
5,7,7,9,10,11,12,14,15,17

Answer 5

Step 1:
5+7+7+9+10+11+12+14+15+17

Step 2:
107 is the total then divide by the total amount of numbers (10)

Step 3:
107 ÷ 10 = 10.7 (the mean)

Question 6

What is a strength of the mean? (representative)

Answer 6

The mean is more representative of the data as it includes all of the scores/values in the data set within the calculation

Question 7

What is a limitation of the mean? (reliability)

Answer 7

The mean can be easily distorted by extreme values, so does not have complete reliability

Question 8

What is the median?

Answer 8

The median is the middle value in the data set when scores are arranged from lowest to highest

Question 9

How is the median calculated?

Answer 9

When there is an odd number of values the median is easily identified

In a set of even numbered scores, the median is halfway between the two middle scores

Question 10

What is a strength of the median? (unaffected values)

Answer 10

An advantage of using the median is that extreme scores do not affect the value, allowing the median to remain the same no matter how extreme the values. The median is also very easily calculated

Question 11

What is a limitation of the median? (sensitivity)

Answer 11

The median is less sensitive than the mean because it does not include all the scores in the final calculation

Question 12

How is the mode calculated?

Answer 12

The mode is calculated by placing the numbers in order and having the most common number identified

Question 13

What is the mode?

Answer 13

The mode is the most frequently occurring score/value within a set of data

Question 14

What are some anomalies that present themselves when calculating the mode?

Answer 14

In some data sets there may be two modes (bi - modal) or no mode if all the scores are different

Question 15

What is a limitation of using the mode? (representation)

Answer 15

The mode is a very crude measure. It can be affected a change of one score and is sometimes not representative of the whole data

Question 16

What is a strength of using the mode? (extreme value)

Answer 16

The mode result does not tend to be unaffected by extreme values

Question 17

What are the measures of dispersion?

Answer 17

The measures of dispersion are the general term for any measure if the spread or variation in a set of scores

Question 18

How many types of measures of dispersion do you need to consider?

What are the names of the different measures of dispersion?

Answer 18

There are two measures of dispersion to consider;

1. Range
2. Standard deviation

Question 19

What is the range?

Answer 19

The range is the calculation used to work out the spread of scores by taking the lowest value from the highest value then adds one

Question 20

What is the range of the following numbers:

0, 47, 49, 50, 50, 51, 53, 54, 56, 56, 57, 100

Answer 20

100 - 0 = 100
100 + 1 = 101

Question 20

What is the strength of using the range? (minimum effort)

Answer 20

The range is quick to obtain as it is easy to calculate

Question 21

What is a limitation of using the range? (representation)

Answer 21

The range only takes into consideration the two most extreme values, which may be unrepresentative of the data set as a whole

Question 22

What is standard deviation?

Answer 22

Standard deviation is a single value that tells us how far scores deviate from the mean

Question 23

As standard deviation grows, what does this show?

Answer 23

As standard deviation becomes larger, it shows a greater dispersion or spread of the set of data

Question 24

What does a low standard deviation reflect?

Answer 24

A low standard deviation value reflects the fact that the data may be tightly clustered around the mean, which might imply that all participants responded in a fairly similar way

Question 24

What is a strength of using the standard deviation? (precise measure)

Answer 24

The standard deviation is a much more precise measure of dispersion than the range as it includes all values within the final calculation

Question 25

What is a limitation of using the standard deviation? (distortion)

Answer 25

The standard deviation tends to be distorted by a single extreme value