The correct answers are a), f) and h). A measure of central tendency is an ‘expected’ or ‘average’ value of a distribution that is used to help to summarise a variable. A measure of central tendency is often presented alongside an appropriate measure of dispersion. The mean is quoted for normally distributed data and the median where the data is not normally distributed (non parametric).The mode is rarely reported.

 The correct answer is c). Add up all of the numbers and then divide by the number of values. (141 + 155 + 130 + 146 + 141 + 134)/ 6 = 847 / 6 = 141.16666. The mean is therefore 141.17cm to 2 decimal places (2dp).

 The correct answer is b). The Median is the middle value once the data have been sorted from smallest to largest. The sorted data would look like this: 130, 134, 141, 141, 146, 155. When we have an odd number of values the median is simply the middle value. Here we have an even number of values, so the median is the mean of the middle two values. (141+141)/2 = 242/6 = 141. The median is therefore 141cm.

 The correct answer is b). The Mode is he most frequently occurring value. Here we have two children who are 141 cm tall, whereas all of the other heights only occur once. The mode is therefore 141cm.

 The correct answer is c). The bar chart is used to display the frequencies of items for a categorical variable, in this example colour. The most suitable measure of location for this type of variable is the mode which indicates the most frequent occurring category.

 The correct answer is a). The histogram is used to display the distribution of a continuous variable. It is showing a bell-shaped distribution, suggesting it has a Normal distribution. The mean is the most suitable measure of location for this type of variable with such a distribution.

 The correct answer is b). The histogram is used to display the distribution of a continuous variable. It is showing a skewed distribution, suggesting there are some outliers in the data. The median is the most suitable measure of location for this type of variable with such a distribution since it is calculated by taking the middle value of the ranked data and is not affected by outliers or extreme values whereas the mean is.

 The correct answer is a). When there are even numbers of observations in a variable, the median is the average of the middle two values of the ordered data in a variable. The mode is normally used to represent the most frequent observation in a categorical variable. The median is the middle value of the ordered data, and it is not affected by exceptionally small or large values in the data, hence it is not sensitive to outliers and extreme values.

 The correct answers are a), c) and d). b) The mean is highly affected by the outliers and extreme values when the distribution is skewed; therefore, it should not be reported as the measure of central tendency for data with a skewed distribution. c) The median is not sensitive to outliers and extreme values, so it should be reported as the measure of central tendency for data with a left (or right) skewed distribution.

 The correct answers are a) and d). a) is correct, but note that this is only true when the distribution is symmetric and Normal. b) A variable with a negatively skewed distribution is one that has some relatively small values in the data compared to the rest of the data. The mean will therefore tend to be smaller than the median. c) It is not necessary to report all the measures of location. The types of data should first be identified. If it is categorical data, then use the mode. If it is continuous data, then the distribution of the variable should be assessed. d) If it is normally distributed data, report the mean; however, if the data is skewed, then both mean and median could be reported.