FS Maths Level 2 – July 15, 2023 (Handling information and data-2).
- 1. Topics for today’s class: Mean Median Mode Ranges Scatter Graphs
- 2. Mean, Median, Mode and Range
- 3. The mean is the total of the numbers divided by how many numbers there are. • To find the mean, add all the numbers together then divide by the number of numbers. • E.g 6 + 3 + 100 + 3 + 13 = 125 ÷ 5 = 25 • The mean is 25. • The mean is not always a whole number.
- 4. The median is the middle value. • To find the median, order the numbers and see which one is in the middle of the list. • E.g 3, 3, 6, 13, 100 = 6 • The median is 6. • If there are two middle values the median is halfway between them. This might not be a whole number. The mode is the number that appears the most. •To find the mode, order the numbers lowest to highest and see which number appears the most often. •E.g 3, 3, 6, 13, 100 = 3 •The mode is 3.
- 5. The range is the difference between the biggest and the smallest number. • To find the range, subtract the lowest number from the biggest number. • E.g 3, 3, 6, 13, 100 SO, 100 - 3 = 97 • The range is 97.
- 6. Practice Question Question A die is thrown 10 times. These are the results: 3, 5, 1, 2, 6, 4, 2, 5, 6, 1 What is the mean score? Question Find the median of each of the following sets of numbers: a) 2, 4, 7, 1, 9, 3, 11 b) 4, 1, 3, 6, 9, 10 Question Find the mode of each of the following sets of numbers: a) 3, 7, 1, 3, 4, 8, 3 b) 2, 7, 2, 1, 4, 7, 3 Question Find the range of the following set of numbers: a) 23, 27, 40, 18, 25 b) 25, 26, 57, 15, 47
- 7. Answers To find the answer, add the values together and divide the total by the number of values: Mean =(3+5+1+2+6+4+2+5+6+1)÷10 35÷10=3.5 a) Place these numbers in order: 1, 2, 3, 4, 7, 9, 11 The middle number is 4. Therefore the median is 4. b) Place these numbers in order: 1, 3, 4, 6, 9, 10 There are two middle numbers (4 and 6), so we find the mean of these two numbers. The median is therefore: (4+6)÷2=5
- 8. a) Start by placing the numbers in order: 1, 3, 3, 3, 4, 7, 8 The number 3 occurs most often so the mode is 3. b) Start by placing the numbers in order: 1, 2, 2, 3, 4, 7, 7 The numbers 2 and 7 occur more often so the modes are 2 and 7. a) The largest value is 40 and the smallest value is 18. Therefore, the range is 40−18=22. b) The largest value is 57 and the smallest value is 15. Therefore, the range is 57−15=42.
- 9. Data Analysis – Scatter Diagrams Scatter diagrams are used to examine whether two pieces of data are linked or related. The word used to describe this relationship is correlation. Correlation is measured in terms of type and strength. The different types of correlation are described as positive, negative or zero correlation. The strength of the correlation is described as strong or weak. When a scatter diagram shows correlation between the two sets of data, a can be drawn to highlight the trend of data ‘line of best fit’
- 10. Correlation If there is a relationship between two variables, we say there is a correlation. There are two types of correlation: Positive correlation – as one variable goes up, the other also goes up. Negative correlation – as one variables goes up, the other goes down. If the points are randomly spread, we say there is no correlation.
- 11. Drawing Scatter Graphs Example: The table below shows the results of students’ Maths and English exams out of 100. Plot a scatter graph for this information. Draw the axes. One should be for the ‘Maths mark’, making sure it goes up to at least 100 and the other should be for the ‘English Mark’, making sure it goes up to at least 100100 also. Label the axes. Then, plot the data as shown on the graph to the right e.g. for someone who got 38 on their maths exam and 74 on their English exam, go across to 38 on the x-axis and then up to 74 on the y-axis, and draw a cross or a dot.
- 12. Drawing a Line of Best Fit A line of best fit is a straight line that is used to represent the correlation of the data. Lines of best fit should go through the middle of all the points, with an equal number of points on either side of the line. Note: Make sure you use a sharp pencil and a ruler when drawing a line of best fit.
- 13. Practice Question John records the temperature of a cup of coffee over time. The results are shown in the table below: a) Draw a scatter graph for the data. b) State the type of correlation. c) Estimate the temperature of a cup of coffee after 66 minutes.