**Quantitative Data Analysis – Measures of Central Tendency (Description, AO1)**

When you carry out a psychological experiment, you end up with a great deal of RAW DATA, usually in the form of 2 sets of scores – one for each condition. The two sets of scores need to be compared to see if there is a noticeable difference between them. Often, you need to summarise this data so that you can easily see if your study has been successful.

A set of scores can be summarised by:-

1) A measure of ** central tendency** (or

**) of the scores.**

*average*2) A measure of the

*(or*

**dispersion****) of the scores. A measure of dispersion is a number which indicates how far each individual score (in the raw data set) is from the mean, (i.e. how far each score in the raw data set deviates from the mean).**

*spread*There are **3 measures of central tendency:** the mean, median and mode.

* 1) MEAN (AO1)*– This is calculated by adding up all the scores in a group/ in the raw data set and dividing it by the number of participants. It can only be used when the data is at interval level.

* For example:* Imagine the following are scores from a memory test (out of 20) obtained from a group of teenagers (age 13 to 19 inclusive);

19, 18, 19, 20, 15, 16, 11, 14, 12, 19, 18, 19, 17, 12 (there are 14 participants in this research study)

In order to calculate the mean of these scores (the average memory performance of teenagers aged 13 to 19 in this study), we need to add all the above scores. This gives us a total of – 229

In order to calculate the mean, the total of the scores (229) needs to be divided by the number of participants in the study, which in this case is 14.

229/14 = 16.4, therefore, the * mean* memory performance in this study is

*.*

**16.4**

**Evaluation (AO3) of the Mean as a Measure of Central Tendency **

**Strength of using the Mean:**

**POINT:** The mean can be considered an accurate and sensitive measure of the average of a set of scores. **EXAMPLE: ***For example,* the mean takes all the scores in the data set into consideration. **ELABORATION: ***This is a strength because, *due to the fact that all the scores are taken into consideration, it can be seen that the mean is a highly representative measure of central tendency and therefore is an accurate representation of the whole data set.

**Weakness of using the Mean:**

**POINT:** A weakness of using the mean is that it can be influenced by rogue scores. **EXAMPLE:** *For example, *in a set of data with similar scores (e.g. 13, 12, 11, 10 etc…) a score like 5 can be seen as a rogue score that will significantly lower the average (mean) calculation. **ELABOATION:** *This is a weakness because, *rogue scores in the data set can significantly increase/ reduce the calculated mean score making it unreflective/unrepresentative of the raw data set.

* 2) MEDIAN (AO1)*– This is the middle score. It is calculated by putting the scores in numerical order and finding the middle value. If there is an even number of scores, the two middle scores are averaged to find the median. It can only be used when the data is of at least ordinal level.

** For example, **in order to calculate the mean of the data below

19, 18, 19, 20, 15, 16, 11, 14, 12, 19, 18, 19, 17, 12 the scores are first arranged in ascending order,

11, 12, 12, 14, 15, 16, 17, 18, 18, 19, 19, 19, 19, 20 – now the middle * (median) value* of this data set can be established which, in this case is

**17.5.**

**Evaluation (AO3) of the Median as a Measure of Central Tendency **

__Strength__** of using the Median:**** **

* POINT:* A strength of using the median is that it is unaffected by extreme, rogue scores.

*EXAMPLE:**For example,*the median is only concerned with the middle number in a set of raw data, it doesn’t consider any of the other scores.

*ELABOATION:**This is a strength because,*only considering the middle score means that any other scores (in particular, rogue/extreme scores) are ignored, this makes the median more representative of the whole data set and therefore, the median can be said to be an accurate measure of central tendency.

*Weakness of using the Median:*

**POINT:** A weakness of using the median is that it doesn’t take all the scores in the data set into consideration. **EXAMPLE:** For example, the median is only concerned with the middle number in a set of raw data, it doesn’t consider any of the other scores. ** ELABOATION:** This is a weakness because, only considering the middle score means that all other scores in the data set are ignored, from this, the accuracy of the median can be questioned – how can this be an accurate measure of central tendency if it doesn’t take all the scores in the data set into consideration?

** 3) MODE (AO1)-** This is the most common score/the score that appears the most in a set of raw data. It can be used with any level of data, because it requires only at least nominal data.

For example, in the following set of data:

19, 18, 19, 20, 15, 16, 11, 14, 12, 19, 18, 19, 17, 12 the * mode *is

*This is because the number 19 appears more frequently than any other in this set of data.*

**19.***Evaluation (AO3) of the Mode as a Measure of Central Tendency*

**Strength of using the Mode:** **POINT:** A strength of using the mode is that it is unaffected by extreme, rogue scores. **EXAMPLE:** For example, the mode is only concerned with the most frequently occurring number in a set of raw data, it doesn’t consider any of the other scores. **ELABOATION:** This is a strength because, only considering the most frequently occurring number means that any other scores (in particular, rogue/extreme scores) are ignored, this makes the mode more representative of the whole data set and therefore, the mode can be said to be an accurate measure of central tendency.

*Weakness of using the Mode:*

**POINT:** A weakness of using the mode is that it doesn’t take all the scores in the data set into consideration. **EXAMPLE:** For example, the mode is only concerned with the most frequently occurring number in a set of raw data, it doesn’t consider any of the other scores. **ELABOATION:** This is a weakness because, only considering the most frequently occurring score means that all other scores in the data set are ignored, from this, the accuracy of the mode can be questioned – how can this be an accurate measure of central tendency if it doesn’t take all the scores in the data set into consideration?