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Measures of Central Tendency and Dispersion. Measures of central tendency. Which measure of central tendency?. Measures of dispersion - range. Measures of dispersion show how the data is spread out. There are two types of measure of dispersion: range and standard deviation.
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Measures of dispersion - range Measures of dispersion show how the data is spread out. There are two types of measure of dispersion: range and standard deviation. The range is a measure of the spread of the dataset. It can be calculated by subtracting the lowest number in the dataset from the highest number of the dataset. The range gives an indication of reliability. A small range means the experiment has produced several similar data points. Range is easily skewed by a single very large or small value.
Standard deviation The standard deviation shows the average distance from the mean of all the data points. It is a measure of variation. Unlike the range, standard deviation is not distorted by outliers. The measure uses all of the data points to calculate the variation from the mean, so it is a more accurate measurement. If a dataset for an experiment has a low standard deviation, it means that all of the data points are close to the mean and it is a reliable test. formula for standard deviation: For example, if you look at a set of exam results the standard deviation will tell you how different the marks of the whole class are.
Task • Create a paper aeroplane in 2 minutes. Write your name on it CLEARLY • There are no rules apart from that it must be made from paper no larger than A4
Calculating quantitative data • You will now throw your plane. • The distance will be measured and written on the whiteboard next to your name. • You must calculate: • Mean • Mode • Median • Range • How could this data be represented in a graph?
Data Distributions • If we are plotting frequency data, we may start to see patterns arise in a data distribution. • The larger the data set, the more likely these distributions are to occur. • These distributions are generally classed as normal or skewed.
Data Distributions • Normal Distribution • Most results cluster around the mean • A few very high and a few very low. • Often called a bell curve • 68.26% of people will be within one SD of the mean • 95.44% will be within two SD of the mean • 99.74% are within three SD. • 0.26% will beyond three SD.
Think of other examples where we would expect a normal distribution.
Data Distributions • Skewed Distribution • Not all data will be a normal distribution • Data may cluster around high or low scores, skewing the bell curve • This affects the mean, median and mode
Data Distributions • Negatively Skewed: • A few extreme low scores • A skew towards high scores. • Long tail on the left. • The mode is greater than the mean. • Eg. Results for an easy maths test • Very few students did poorly on the test. • Most scored high, meaning the distribution is skewed to the left.
Data Distributions • Positively Skewed: • A few extreme high scores • A skew towards low scores. • Long tail on the right. • The mean is greater than the mode. • Example: how long people admitted to hospital stay before being discharged. • Very few patients stay for an extended period. • Most are discharged after a few days, meaning the distribution is skewed to the right.
Challenge Task • Complete the graphs card sort game.
