1. Starter List 5 types of continuous data List 3 types of discrete data Find the median of the following numbers: 2, 3, 6, 5, 7, 7, 3, 1, 2, 5, 4 Why is the value for the mean calculated from grouped frequency table an estimate?

2. Grouped Data Time (minutes)Frequency 17-184 18-197 19-208 20-2113 21-2212 22-239 23-247 Total = 60

3. Finding the Mean Time (minutes) Frequency f 4 7 8 13 12 9 7 Total = 60 17 ≤ t < 18 18 ≤ t < 19 19 ≤ t < 20 20 ≤ t < 21 21 ≤ t < 22 22 ≤ t < 23 23 ≤ t < 24 Midpoint t 17.5 18.5 19.5 20.5 21.5 22.5 23.5 t x f 17.5 x 4 = 70 18.5 x 7 = 129.5 19.5 x 8 = 156 20.5 x 13 = 266.5 21.5 x 12 = 256 22.5 x 9 = 202.5 23.5 x 7 = 164.5 Total = 1247 mean = 1247 60 = 20.8 (3s.f.)

4. Continuous Data Data that can take any value (within a range) Examples: time, weight, height, etc. 0time (for example) You can imagine the class boundaries as fences between a continuous line of possible values 2468 These classes would be written as: 0 ≤ t < 2 2 ≤ t < 4 4 ≤ t < 6 6 ≤ t < 8 8 ≤ t < 10 10 Each class has: An upper bound A lower bound A class width A midpoint

5. Discrete Data Data that can only take certain values Examples: number of people, shoe size. 0n, number of people There are only certain values possible. Classes are like a container that hold certain values 2468 These classes would be written as: 0 - 1 2 - 3 4 - 5 6 - 7 8 - 9 10 - 11 10 Each class has: An upper bound A lower bound A class width A midpoint 1197531

6. Cumulative Frequency Time (minutes) Frequency f 4 7 8 13 12 9 7 Total = 60 17 ≤ t < 18 18 ≤ t < 19 19 ≤ t < 20 20 ≤ t < 21 21 ≤ t < 22 22 ≤ t < 23 23 ≤ t < 24 Time (minutes) Frequency f 4 17 ≤ t < 18 17 ≤ t < 19 17 ≤ t < 20 17 ≤ t < 21 17 ≤ t < 22 17 ≤ t < 23 17 ≤ t < 24 11 19 32 44 53 60

7. Time (minutes) Frequency f 4 17 ≤ t < 18 17 ≤ t < 19 17 ≤ t < 20 17 ≤ t < 21 17 ≤ t < 22 17 ≤ t < 23 17 ≤ t < 24 11 19 32 44 53 60 1718192021222324 10 20 30 40 50 60 Cumulative Frequency Curve plot points at the upper limit of each class Line is a smooth curve NOT straight lines between each point f t

8. The Median and the Quartiles The median is the middle value. Another way of thinking about it is to consider at what value exactly half of the samples were smaller and half were bigger. We also look at the quartiles: The lower quartile is the value at which 25% of the samples are smaller and 75% are bigger. If we had 60 runners in a race, it would be the time the 15 th runner finished, 25% were quicker, 75% were slower. The upper quartile is the value at which 75% of the samples are smaller and 25% are bigger. Again, for 60 runners, it would be the time the 45 th person finished. 75% were quicker, 25% were slower. The interquartile range (IQR) = upper quartile – lower quartile = Q 3 – Q 1 The IQR gives a measure of the spread of the data. Q 1 is the first quartile, or the lower quartile Q 2 is the second quartile, or the median, m Q 3 is the third quartile, or the upper quartile

9. 1718192021222324 10 20 30 40 50 60 Finding the median f t Median = m or Q 2 We find the value of t when f = 30 Upper quartile = Q 3 We find the value of t when f = 45 Lower quartile = Q 1 We find the value of t when f = 15 Q1Q1 Q2Q2 Q3Q3

10. Interquartile Range The interquartile range (IQR) = upper quartile – lower quartile = Q 3 – Q 1 The IQR gives a measure of the spread of the data. The data between Q 1 and Q 3 is half of the samples. How packed together are these results? The IQR gives us a measure of this. If the IQR is small, the cumulative frequency curve will be steeper in the middle. This means that more samples are nearer to the mean, If the IQR is large, the cumulative frequency curve will not be so steep in the middle. The samples are more spread out.

11. Page 320 Exercise 117 Questions 13, 14, 15 & 16

12. PRINTABLE SLIDES Slides after this point have no animation.

13. Cumulative Frequency Time (minutes) Frequency f 4 7 8 13 12 9 7 Total = 60 17 ≤ t < 18 18 ≤ t < 19 19 ≤ t < 20 20 ≤ t < 21 21 ≤ t < 22 22 ≤ t < 23 23 ≤ t < 24 Time (minutes) Frequency f 4 17 ≤ t < 18 17 ≤ t < 19 17 ≤ t < 20 17 ≤ t < 21 17 ≤ t < 22 17 ≤ t < 23 17 ≤ t < 24 11 19 32 44 53 60

14. Time (minutes) Frequency f 4 17 ≤ t < 18 17 ≤ t < 19 17 ≤ t < 20 17 ≤ t < 21 17 ≤ t < 22 17 ≤ t < 23 17 ≤ t < 24 11 19 32 44 53 60 1718192021222324 10 20 30 40 50 60 Cumulative Frequency Curve plot points at the upper limit of each class Line is a smooth curve NOT straight lines between each point f t

15. The Median and the Quartiles The median is the middle value. Another way of thinking about it is to consider at what value exactly half of the samples were smaller and half were bigger. We also look at the quartiles: The lower quartile is the value at which 25% of the samples are smaller and 75% are bigger. If we had 60 runners in a race, it would be the time the 15 th runner finished, 25% were quicker, 75% were slower. The upper quartile is the value at which 75% of the samples are smaller and 25% are bigger. Again, for 60 runners, it would be the time the 45 th person finished. 75% were quicker, 25% were slower. The interquartile range (IQR) = upper quartile – lower quartile = Q 3 – Q 1 The IQR gives a measure of the spread of the data. Q 1 is the first quartile, or the lower quartile Q 2 is the second quartile, or the median, m Q 3 is the third quartile, or the upper quartile

16. 1718192021222324 10 20 30 40 50 60 Finding the median f t Median = m or Q 2 We find the value of t when f = 30 Upper quartile = Q 3 We find the value of t when f = 45 Lower quartile = Q 1 We find the value of t when f = 15 Q1Q1 Q2Q2 Q3Q3

17. Interquartile Range The interquartile range (IQR) = upper quartile – lower quartile = Q 3 – Q 1 The IQR gives a measure of the spread of the data. The data between Q 1 and Q 3 is half of the samples. How packed together are these results? The IQR gives us a measure of this. If the IQR is small, the cumulative frequency curve will be steeper in the middle. This means that more samples are nearer to the mean, If the IQR is large, the cumulative frequency curve will not be so steep in the middle. The samples are more spread out.