1 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use Measures of Spread Stage 6 - Year 12 General Mathematic (HSC)

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1 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use Measures of Spread Stage 6 - Year 12 General Mathematic (HSC)

2 The Mean Mean The Mean is a measure of central tendency Mean = Sum of the Scores Number of the Scores Example: 2, 3, 5, 4, 7, 6, 8. Mean = 2+3+5+4+7+6+8 7 35 7 = = 5 End of Slide

3 The Median Median The Median is a measure of central tendency The Median is the middle score, Example: 2, 3, 4, 5, 7, 7, 8. Median = 5 when the scores are in order. End of Slide

4 Example: 2, 3, 4, 5, 7, 7, 8, 8. = 6 Median = 5+7 2 End of Slide The Median Median The Median is a measure of central tendency The Median is the middle score, when the scores are in order.

5 The Range Example: 2, 3, 4, 5, 7, 7, 8, 8. Rangespread The Range is a measure of spread. Range = Highest Score - Lowest Score, Range = 8 - 2 = 6 Highest Score,Lowest Score, End of Slide

6 Median = 5 The Interquartile Range The Interquartile Range 2, 4, 4, 5, 6, 7, 7. The difference between the upper quartile and the lower quartile. The quartiles are found by dividing the ordered data in half and then quarters. The IQR measures the middle 50% of scores Lower QuartileUpper Quartile Q1 Q3 IQR = Q3 - Q1 = 7 - 4 = 3 End of Slide

7 2, 3, 5, 5, 7, 7, 9, 9. (Data must be in order) Median = Q1 = Q3 = IQR =Q3 - Q1 =8 - 4 =4 5+7 2 = 6 3+5 2 = 4 7+9 2 = 8 End of Slide TheInterquartile Range The Interquartile Range

8 The Mode The Mode is a measure of central tendency. The Mode is the most common score, Example 1: 2, 3, 4, 5, 7, 7, 8. highest frequency the score with the highest frequency. Mode = 7 Example 2: 2, 3, 4, 5, 7, 7, 8, 8. Mode = 7, 8 Polymodal End of Slide More than one Mode Press

9 Finding the Mean Using a Table. Scorex Tally Freq fx f 1 2 3 4 5 Σf =Σfx = 3 4 7 6 2 1x33 2x48 3x721 4x624 5x210 2266 Σfx ΣfΣf x = 66 22 = = 3 x x x x x End of Slide

10 Finding the Mean for Grouped Data Class 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-40 Class Centre cc (0+4)÷22 (5+9)÷27 (10+14)÷212 (15+19)÷217 (20+24)÷222 (25+29)÷227 (30+34)÷232 (35+40)÷237 Tallyff.cc Σf=Σf= Σf.cc= 2 3 1 4 3 4 2 1 20 2x2 4 7x3 21 12x1 12 17x4 68 22x3 66 27x4108 32x2 64 37x1 37 380 Σf.cc ΣfΣf x = 380 20 = = 19 End of Slide

11 Finding the Median for Grouped Data Finding the Median for Grouped Data Class 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-40 Class Centre cc 2 7 12 17 22 27 32 37 Tallyfcf 2 3 1 4 3 4 2 1 2 2+3 5 5+1 6 6+4 10 10+313 13+417 17+2 19 19+1 20 There are 20 scores. 10 th 11 th Therefore the median is the 10 th and 11 th scores. 10 th 10 th = 17 11 th 11 th = 22 Median = 17+222 = 19.5 End of Show

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