Averages Mathematics for GCSE Science This presentation covers these Maths skills: find arithmetic means understand the terms mean, mode and median. 1 of 16 Copyright AQA and its licensors. All rights reserved. How can we summarise data? When carrying out an investigation, data collected must recorded so that conclusions can be made. This data can be displayed using tables, from which graphs can be drawn. Finding the average helps you to draw conclusions from data. A measure of average is a number that is typical for a set of figures. The averages most commonly used are: MEAN MEDIAN MODE 2 of 16 Copyright AQA and its licensors. All rights reserved. Do you know the definitions, and which is which?
Mean Most common value Median Middle value in an ordered list Mode Sum of all values number of values See BBC Bitesize for a recap of these concepts: BBC Bitesize - Measures of average YouTube - Mean, Median and Mode 3 of 16 Copyright AQA and its licensors. All rights reserved. Why are averages important? If we do an experiment just once, it is probable that the result will vary from the true value. The experiment is repeated to get a set of values all of which may vary from the true value.
An average is then calculated so a conclusion can be made. A typical question might be to compare two data sets using the mean, median or mode. You would be asked which data set has a higher/lower value, and asked to interpret this result in the context of the data. 4 of 16 Copyright AQA and its licensors. All rights reserved. Using the mean Nitrate fertilisers are soluble in water and can be washed off fields and into rivers and reservoirs by rainwater. Samples were taken from 2 different rivers at 5 different points in time. The following table shows the nitrate levels at each point. Anything higher than 10 mg/l is considered unsafe. River Level of nitrate (mg/l) Trial 1 Trial 2
Trial 3 Trial 4 Trial 5 A 15 13 11 9 7 B 9 8
9 10 11 What is the mean level of nitrate for each river? Evaluate if the mean level of nitrate in each river is unsafe. 5 of 16 Copyright AQA and its licensors. All rights reserved. Answers What is the mean level of nitrate for each river? For river A: 15 + 13 + 11 + 9 + 7= 55 55 5 = 11 The mean level of nitrate for River A is 11 mg/l For river B: 9 + 8 + 9 +10 + 11 = 37 37 5 = 7.4
The mean level of nitrate for River B is 7.4 mg/l Evaluate if the mean level of nitrate in each river is unsafe. Anything higher than 10 mg/l is considered unsafe. The mean level of nitrate in river A is above 10 mg/l, so is unsafe. The mean level of nitrate in river B is below 10 mg/l, so is safe. 6 of 16 Copyright AQA and its licensors. All rights reserved. Using the median An experiment was carried out into the strength of rubber. 7 strips were stretched until they snapped. The following table shows what length each sample reached. Sample number Length (mm) 1 21
2 5 3 22 4 25 5 27 6 26 7
28 7 of 16 Copyright AQA and its licensors. All rights reserved. Calculate the median length reached by the strip. How does this compare to the mean value? Why are the median and mean so different? Why wouldnt you use the mode for this data? Answers Calculate the median length reached by the strip. Put the numbers in order: 5, 21, 22, 25, 26, 27, 28 Choose the middle number. The median length is 25mm.
How does this compare to the mean value? 5 + 21 + 22 + 25 + 26 + 27 + 28 = 154 154 7 = 22 The mean value is 22mm. Why are the median and mean different? This is because the mean is skewed by the outlier 5. The median is not affected by this. Why wouldnt you use the mode for this data? No two numbers are the same, so it would not be possible to use the mode. 8 of 16 Copyright AQA and its licensors. All rights reserved. Using the mode A study was carried out to find the average height of children in a certain class. The results are shown in the following table. Height, h, (cm)
Number of females Number of males Total number of students 140 < h 144 4 - 4 144 < h 148 5 -
5 148 < h 152 4 4 8 152 < h 156 1 6 7 156 < h 160 2 3
5 160 < h 164 - 1 1 What is the modal height of a student in this class? How does this compare to the modal height of a male student and a female student? What does this tell you about using the mode? 9 of 16 Copyright AQA and its licensors. All rights reserved. Answers What is the modal height of a student in this class?
The most common height is 148 < h 152, with 8 students falling within that interval. How does this compare to the modal height of a male student and a female student? The modal height of a male student is 152 < h 156 The modal height of a female student is 144 < h 148 What does this tell you about using the mode? Using the mode does not always give a good representation of the data. 10 of 16 Copyright AQA and its licensors. All rights reserved. Advantages and disadvantages The mean, median and mode all have advantages and disadvantages. Can you think what they are? Advantages Disadvantages
Mean Uses all the data Usually most representative Isnt always a data value May be distorted by extreme data values Median Easy to find in ordered data Not distorted by extreme data values Isnt always a data value Not always a good representation of the full data set
Mode Easy to find in tallied data Always a data value Doesn't always exist, or sometimes more than one Not always a good representation of the data 11 of 16 Copyright AQA and its licensors. All rights reserved. Some questions to try from Exampro GCSE Maths F 12 of 16 Copyright AQA and its licensors. All rights reserved. GCSE Maths F 13 of 16
Copyright AQA and its licensors. All rights reserved. GCSE Biology sample assessment materials 14 of 16 Copyright AQA and its licensors. All rights reserved. GCSE Biology sample assessment materials 15 of 16 Copyright AQA and its licensors. All rights reserved. GCSE Biology sample assessment materials 16 of 16 Copyright AQA and its licensors. All rights reserved.
Corresponding Angles 70 a 70 b 110 What are the values of letters a and b? Angles Corresponding Angles Created by Mr.Lafferty Math Dept Created by Mr.Lafferty Math Dept Created by Mr.Lafferty Math Dept Created by Mr.Lafferty Math Dept
Word: Cacophony. Definition: a harsh mixture of sounds. Part of Speech: noun. Example Sentence: The class could not hear the teacher over the cacophony of sounds coming from the unpracticed band in the room next door.
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