1. Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

2. The mode of a data set is the value that occurs most frequently. The median of a data set is the value that lies in the middle when the data are arranged in size order. The mean of a data set is the sum of all the values divided by the number of values. Measures of Central Tendency

3. Mode – the value that occurs most frequently – data can be bimodal – data can have no mode – is not affected by extreme values – is always a member of the set of data Measures of Central Tendency

4. M ean –i–i s what we know as the average –s–s ymbol:, x bar –i–i s generally a good representative of the data –c–c an be influenced by extreme values

5. M edian –t–t he middle number (data must be ordered) –m–m edian of an odd number of data is one of the data –m–m edian of an even number of data is the mean of the two middle values n ot necessarily one of the data –i–i s not affected by extreme values

6. Here is a set of data: 5 4 8 4 4 7 8 9 11 1 5 Find the mode, median and mean Problem 1 Mode = 4 since it occurs the most number of times (3 times) Median = 5 arrange data in size order 1 4 4 4 5 5 7 8 8 9 11 There are 11 entries, thus the median is the (11+1) ÷ 2 = 6 th value Mean = 6 sum of all the values (66) divided by the number of values (11), thus 66 ÷ 11 = 6

7. The mean of the ten numbers listed below is 5.5. 4, 3, a, 8, 7, 3, 9, 5, 8, 3 (a)Find the value of a. (b)Find the median of these numbers. Problem 2 (b) 3 3 3 4 5 5 7 8 8 9 average middle scores = 5

8. Mean, Mode and Median with a Frequency Table

9. Find the mode. Mode = 7

10. 1.Multiply the value by the frequency. 2.Add products. 3.Divide by the sum of the frequency. To find the mean: f ∙x Find the mean. 3 4 15 42 105 64 45 278 278 ÷ 40 = 6.95

11. 1.Consider the total sample size. 2.Determine the position of the median. 3.Considering the accumulated values, find the median. To find the median: Find the median. The median is the (40+1) ÷ 2 = 20.5 th entry. So it is between the 20 th and 21 st value. Since both of these entries are 7, the median is 7

12. Find the mode, median and mean of these data. Mode = 22 Number of SweetsFrequency 202 213 2213 234 242 Total24 Median = 22Mean = 22.0

13. Mean, Mode and Median for Grouped Data

14. Since we are NOT able to determine the raw data from this table. Use the midpoint of the class. Finding the mean from grouped data.

15. The data below represents the ages of bus drivers. Find the approximate mean to the nearest year. midpoint f ∙x 23 28 33 38 43 48 53 253 392 1056 1026 1247 816 371 5161 5161 ÷ 137 = 37.7

16. The time, in seconds, taken to complete 200 bouts of sumo wrestling are shown in the table. Calculate the modal class and estimate of the mean. Time (t) in SecondsFrequency 0 ≤ t < 2037 20 ≤ t < 4062 40 ≤ t < 6046 60 ≤ t < 8025 80 ≤ t < 10011 100 ≤ t < 1209 120 ≤ t < 1406 140 ≤ t < 1604 Total200 Modal Class 20 ≤ t < 40 Mean 48.2