Lies, Damn Lies & Statistics…….

Aims For all students to be able to calculate the mean, median and mode from a data set For all students to calculate the standard deviation of a data set and evaluate the data for normal distribution

Averages

Can you calculate the average of this data? 800, 805, 806, 799, 799, 800, 802, 804, 809, 801, 803, 799 If you calculated a figure of Then you have calculated an average of this data set correctly But is it the only average we can calculate?

In the previous slide, you calculated the Mean of the data. As well as the mean, there are two other types of average that can be calculated from the data. These are: The Mode and The Median

The Mode The mode is the number which comes up most often in a data set. Looking at the data set, what is the mode of the data? 800, 805, 806, 799, 799, 800, 802, 804, 809, 801, 803, 799 The mode of this data set is 799 as it appears three times in the data set, more than any other number.

Calculate the mode of this set of data

The Median The Median is the central value of the data sets range. Again, looking at the data set from before, what is the median of the data? 800, 805, 806, 799, 799, 800, 802, 804, 809, 801, 803, 799 The correct value for the Median is 801.5

Calculate the median of this set of data

Why do we need averages?

If you bought 6 loaves of bread like the one above, would they all be exactly 800g in weight? Does it matter if they aren’t the same?

Loaf NumberMr MitchellMiss Priestley 1800g785g 2801g800g 3799g 4800g804g 5798g806g 6802g804g Calculate the mean for each set of data to the nearest whole gram

Are both sets the same? Would you be happy selecting a loaf of bread from either of the two sets? Which one would you rather take the loaf from? Why?

Although both sets of data have the same mean, when plotted the graphs appear very different. So the mean of a data set can be misleading. We need a better way at looking at a data set to how spread the data is.

In an ideal data set, all three averages would have the same value. When we have this shaped graph, it is referred to as a Normal Distribution Curve

Standard Deviation

Standard deviation is a way of measuring how far a set of data values is spread about the mean. The lower the number, the less spread there is. It is given by the equation:

Worked example from our bread data: Step 1: work out the values (remember to use the mean from earlier) Mr Mitchell 800g 801g 799g 800g 798g 802g

Step 2: Calculate S using the Standard Deviation formula…

Your task

Does the height of your Asda Cress seedlings follow a normal distribution? Measure at least 30 seedlings Calculate the mean, mode and median Calculate the standard deviation from the mean of your data Plot your data and draw lines on your graph to show +/- 2sd

Dot plot Once you have measured your cress, plot the data on a graph. The type of graph you are going to plot is a dot plot graph. It shows the frequency of each of the results you have obtained. Once you have plotted the data, draw in a curve to show the distribution. Does it follow normal distribution?

Evaluation Does the height of Tesco Cress seedlings follow a normal distribution curve? How have you proved this with your statistical analysis? Peer assess another group’s work, giving 2 strengths and an area for improvement