2.3.3 Descriptive statistics

Question 1

Measures of central tendency

Answer 1

A form of estimation of a mid-point/average in a set of data

Question 2

Mean

Answer 2

The average that is shown by all scores in the data set when they are divided by n.

Question 3

How do you calculate the MEAN

Answer 3

Calculate by adding all the scores in the data set together and dividing the total by the number of scores that were added

Question 4

Median

Answer 4

The mid-point in a set of data that has been placed in order

Question 5

How do you calculate the MEDIAN if there is no ‘middle score’

Answer 5

You should take the two scores either side of the midpoint, add them together and divide the result (sum) by two

Question 6

Mode

Answer 6

The most common value within a set of data

• Use a tally chart, or group the data together, so it becomes apparent which score occurs most frequently

Question 7

Measures of Dispersion

Answer 7

A measure that shows the spread of data, whether it is tightly clustered or has a broader spread

Question 8

Range

Answer 8

A value that shows the spread of data, representing the difference between the lowest and highest scores

Question 9

How do you calculate the RANGE

Answer 9

Take the lowest score from the highest score and add one. Show your workings

Question 10

Standard Deviation

Answer 10

A value that represents the amount of variation of results from the mean score

Question 11

How do you calculate STANDARD DEVIATION

Answer 11

Calculate the sum of x, minus the mean, squared using a table. Divide this by n-1. Then take the square root of this answer to find the standard deviation

Question 12

2 Strengths of MEAN

Answer 12

+ It is necessary for further statistical analysis such as standard deviation
+ It can always be found when using ordinal or above level data

Question 13

2 Weaknesses of MEAN

Answer 13

• It is influenced by anomalous results
• It may produce a ‘nonsense’ value not in the original data set

Question 14

2 Strengths of MEDIAN

Answer 14

+ It is not influenced by anomalous results
+ It can always be found when using ordinal or above level data

Question 15

2 Weaknesses of MEDIAN

Answer 15

• It is not useful in further statistical analysis
• It may produce a ‘nonsense’ value that was not in the original data set

Question 16

2 Strengths of MODE

Answer 16

+ It can be used for data measured on a nominal scale and is not a ‘nonsense’ value
+ The value has definitely occurred in the data set

Question 17

2 Weaknesses of MODE

Answer 17

• There may be more than one result, or no result if the data set is varied
• It may not display what is occurring in the centre of the data set if there is a skewed distribution

Question 18

2 Strengths of RANGE

Answer 18

+ Is relatively easy to calculate (unlike standard deviation).
+ It gives an indication about the consistency/ reliability of the data

Question 19

1 Weakness of RANGE

Answer 19

• It is influenced by anomalous results; this is a problem because only the highest and lowest scores are considered in the calculation
  > limits validity

Question 20

2 Strengths of STANDARD DEVIATION

Answer 20

+ A more sophisticated measure of dispersion - reflects every score in the data set (unlike the range)
+ Gives you an indication of how close the majority of the scores are to the mean in a normal distribution

Question 21

2 Weaknesses of STANDARD DEVIATION

Answer 21

• Time consuming to calculate compared to the mean or range
• Not all scores will be within one standard deviation, so it can be misleading when it comes to anomalies