What a measure of central tendency is

1. A measure of central tendency gives the typical value in a set of data.
2. The three are the mean, the median and the mode.
3. Each reduces a whole set of numbers to one value, and the three can give different values for the same data.
4. The range is a measure of spread rather than of central tendency, because it describes how far apart the scores are.

The mean

1. The mean is found by adding up every value, then dividing by how many values there are.
2. Strength: every score counts towards it, so none of the data is left out.
3. Weakness: one extreme score pulls it towards itself, so the mean can sit where nobody actually scored.
4. Weakness: it needs numbers, so it cannot be used on categories such as favourite subject.
5. It suits data where the scores are fairly evenly spread and there is no outlier.

The median

1. The median is found by putting the values in order of size and taking the middle one.
2. With an even number of values, add the middle two and divide by two.
3. Strength: an extreme score barely moves it, because only the position of a value matters and not its size.
4. Weakness: it leaves out how far apart the other values are, so two very different sets can share the same median.
5. It suits data with an outlier that would pull the mean somewhere misleading.

The mode

1. The mode is the value that appears most often.
2. Strength: it is the one measure that works on categories, such as which mental health service pupils named most often.
3. Strength: it is always a value that somebody actually recorded.
4. Weakness: a set can have two modes or none at all, and the mode leaves out every value except the commonest.
5. It suits a question about the most common result, and data that is not numerical.

The modal class

1. Data is often collected in bands rather than single values, so a frequency table shows how many fall in each band.
2. The modal class is the band with the highest frequency.
3. It is reported as the band itself, such as 7 to 8 hours.
4. An exact mean cannot be recovered from banded data, because the individual values have been lost.
5. A tally chart is the usual way this data arrives, with a totals column giving each frequency.

Choosing a measure of central tendency

1. An outlier is a value that sits far away from the rest of the set.
2. Worked example: five scores of 4, 5, 5, 6 and 30 add to 50, so the mean is 50 divided by 5, which is 10.
3. Four of those five people scored 6 or less, so a mean of 10 describes nobody in the set.
4. The median is the third value in order, which is 5, and that describes the group better.
5. The mode fits data held in categories, and it also answers a question about the most common response.
6. Reporting a measure of central tendency alongside the range tells the reader what is typical and how varied the scores were.

Turning this into marks

1. When a figure and a reason are both asked for, keep them as two separate points, one giving the calculation and one saying what the figure shows about the data.
2. Write the calculation out, so 48 divided by 7 equals 6.86 shows the total and the division as well as the answer.
3. Name the measure and its units, such as a mean of 6.86 words recalled, because a bare number does not secure the knowledge mark.
4. The mark most often lost is giving the frequency when the modal class was asked for, so the answer reads 7 to 8 hours rather than 11.