1. AS 2.9 STATISTICAL INFERENCE 4 INTERNAL CREDITS

2. SAMPLE STATISTICS REVISION Sample statistics are used to analyse and summarise data. This lesson is revision so you will already be familiar with these concepts. Your graphics calculator makes finding these statistics much easier.

3. BABE RUTH EXAMPLE Babe Ruth (1895 – 1948) was a legendary US baseball player renown for his batting. He hit the following number of home runs in each of his seasons playing for the New York Yankees: 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22

4. Averages There are 3 types of averages that summarise the data at the centre. Mean = sum of all numbers ÷ total number of numbers Median = middle number when the numbers are in order Mode = the number that occurs more often than any other

5. Example Calculate the 3 types of averages for Babe Ruth’s home runs while playing for the NY Yankees. 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22 Mean = (54+59+35+41+46+25+47+60+54+46+49+46+49+46+41+34+22)÷15 = 43.9 Median: 1 st order: 22, 25, 34, 35, 41, 41, 46, 46, 46, 47, 49, 54, 54, 59, 60 2 nd the middle number: 46

6. Example continued Mode: The mode is 46 which is the most common data value. Notes: 1.If there are an even number of data values then the median will be the mean of the two middle values. e.g. 2, 4,6, 9, 15, 25. The median is (6+9)/2 = 7.5

7. 2. There can be 1, 2 or no mode. e.g. 2,3,3,4,5,5,6,7. The mode is 3 and 5. 2,3,3,4,5,5,6,6,7. There is no mode.

8. Quartiles Quartiles help give us an idea about how the data is distributed about the median. The LQ is the value that has 25% of the data below and 75% above. The UQ is the value that has 75% of the data below and 25% above.

9. Quartiles To find quartiles: 1.Put the data in order. 2.Identify the median to split the data in two. 3.Excluding the median, halfway through the first half is the LQ. 4.Halfway through the second half is the UQ.

10. Babe Ruth Find the LQ and UQ of the data. 22, 25, 34, 35, 41, 41, 46, 46, 46, 47, 49, 54, 54, 59, 60 Median is 46. Exclude this. Middle of lower set: 22, 25, 34, 35, 41, 41, 46 is 35. LQ=35 Middle of upper set: 46, 47, 49, 54, 54, 59, 60 is 54. UQ=54

11. Measures of Spread Range = Maximum – Minimum Interquartile Range (IQR) = UQ – LQ We will look at a Standard Deviation next lesson.

12. Babe Ruth Calculate the range and IQR for the Babe Ruth data: 22, 25, 34, 35, 41, 41, 46, 46, 46, 47, 49, 54, 54, 59, 60 Range = 60 – 22 = 38 IQR = 54 – 35 = 19

13. Using your Graphics Calculator 1.Select 2 from menu to get to STAT. 2.Delete existing data by pressing F6 (Next) – F4 (Delete all) – F1 (Confirm) 3.Enter data values into column 1. 4.Select F2 (Calculate) – F6 (Set). Check that: 1VAR XList: List 1 and 1VAR Freq 1: 1 5.Press EXE and then F1 6.Read off required values.