**Objectives**

- Be able to calculate key values (see below)
- Be able to use key values within a real world context

**Keywords**: Mean, Mode, Median, Maximum, Minimum, Range, Average Range, Outlier

We use Mean, Median and Mode to give us an indication of the middle value for a set of numbers, hence the term central tendencies.

**Mean Central Tendency **

The mean represents a continuous number and is calculated by add all scores are together then divided the total by the number of scores. For example:

8 + 5 + 20 + 5 + 9 = 47 ÷ 5 = Mean of **9.4**

Examples of continuous data measures:

- Distance
- millimetres
- centimetres
- metres

- Time
- seconds
- minutes
- hours

- Temperature
- degree Celsius
- fahrenheit

**Median Central Tendency**

The median represents an ordered number (ordinal data, scale response) and is calculated by ranking or ordering all scores (small to high) then find the middle number. For example:

5, 5, 8, 9, 20 = Median of **8**

Examples of ordinal data measures:

- likert scale
- star rating

**Mode Central Tendency**

The mode represents a category value (categorical data, yes or no) and is calculated by grouping the scores by their value. The group with the most scores is the mode value. For example:

[5, 5] [8] [9] [20] = Mode of **5**

Examples of categorical data measures:

- male or female
- yes or no
- most prefered item (manufacture, clothing, cars etc…)

**Maximum and Minimum Scores**

Maximum score is the highest score within your dataset

5, 5, 8, 9, 20 = Max Score of **20**

Minimum score is the lowest score within your dataset

5, 5, 8, 9, 20 = Min Score of **5**

**Range**

The range is calculated by subtracting the minimum score from the maximum score. For example

[5, 5, 8, 9, 20] 20 – 5 = Range of **15**

**Outlier **

An outlier is an isolated score which is very different from the rest. The outlier is often identified in a box plot graph. For example:

[5, 5, 8, 9, 20] = Outlier is **20**

The distance between the maximum score (20) and the nearest neighbour (9) is 11 compared to the distance between the minimum score (5) and 9 is 4.

**Comparing The Central Tendencies (gaming station cabinet)**

The findings of this study **indicates **that the maximum height of a gaming station is 20cm and the minimum is 5cm giving a range of 15cm. **Suggesting **that the cabinet space for the gaming station will need to be at least 15cm in height to accommodate most gaming stations. **However**, this would consume 20% of the cabinet.

The most commonly occurring height of a gaming station was 5cm which is 4.4cm smaller then the mean value (9.4cm) and 3cm smaller then the median value (8cm). **Suggesting** that the gaming cabinet space could be reduced to 10cm. Thus reducing the required space to 13%.

A closer inspection of the data **indicates **that most (80%, n4) of the gaming stations have a height less than 10cm compared to 20% (n1) of the gaming stations which have a height greater than 10cm. **This stud****y**** will** classify this score of 20cm as an outlier and the central tendencies will be recalculate. **This will** tighten the cluster around the mean, giving the results a greater validity or strength.

The new maximum gaming station height is 9cm with an unchanged minimum of 5cm giving a range of 4cm. **Suggesting **that the maximum cabinet space for a gaming station is 10cm or 13% of the cabinet.

The most commonly occurring gaming station height is 5cm which is 2.4cm smaller then the mean (7.4cm) and 3cm less them the median (8cm) giving a average range of 3cm. **Suggesting** that a cabinet space which is equal to 10.4cm (mean 7.4cm + average range 3cm) which is 1.4cm greater then the maximum height (9cm) will accommodate all gaming stations.

The median (8cm) support the mean (7.4cm) central tendency in **suggesting** that the cabinet space should be set at the top end of the range as most gaming stations appear to fall there.

**Where Next**

Distribution and Deviation