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Statistic chapter 1 & 2

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Statistic chapter 1 & 2

1. 1. STATISTIC
2. 2. Outline 1. HISTOGRAM  Histogram Frequency Density Polygon and Curve  Polygon  Curve 2. CHAPTER 2  Mode  Median  Cumulative frequency  Mean
3. 3. HISTOGRAM A histogram is a means of displaying continuous data graphically, conveying the general characteristics data  The data shown in the display record the hand-spans, in centimetres of a group of 55 children. 12 0 13 14 5 15 2 5 16 0 1 2 3 4 7 17 0 2 5 9 18 1 2 4 5 6 6 7 8 19 0 2 2 4 5 5 6 8 8 8 9 20 0 2 4 5 6 7 8 9 21 2 3 6 6 7 22 0 1 2 8 23 24 2 25 26 2 5 9
4. 4.  Consider the following representation of the data in tabulation. Class Frequency Class Width Frequency Density 12 ≤ x < 16 4 4 1 16 ≤ x < 18 10 2 5 18 ≤ x < 19 8 1 8 19 ≤ x < 20 11 1 11 20 ≤ x < 21 8 1 8 21 ≤ x < 23 9 2 4,5 23 ≤ x < 27 4 4 1
5. 5. Consider the following representation of the data in a histogram. 12 10 8 Frequency density 6 4 2 0 15 20 25 Hand-spans (cm)
6. 6.
7. 7.  Construct a histogram to display these data using the classes given Class Frequency 0 ≤ x < 0.5 12 0.5 ≤ x < 1.5 32 1.5 ≤ x < 2.5 20 2.5 ≤ x < 4.5 20 4.5 ≤ x < 6.5 6 6.5 ≤ x < 10.5 2
8. 8. Solution The first step is to calculate the width of each of the classes. The first class is of width 0.5, the next of width 1.0 and so on. The result of these two steps are recorded in the expanded table below. Class width Class Frequency Frequency density 0 ≤ x < 0.5 12 0.5 12:5 = 24 0.5 ≤ x < 32 1 32 1.5 1.5 ≤ x < 20 1 20 2.5 2.5 ≤ x < 20 2 10 4.5 4.5 ≤ x < 6 2 3 6.5
9. 9.  4 0 3 0 Frequency 2 density 0 1 0 0 1 2 3 4 5 6 7 8 9 1 11 1 0 2
10. 10. Frequency Density Polygon and Curve  Polygons The frequency polygon from histogram for these data would like this. 12 12 10 10 8 8 Frequency Frequency 6 6 density density 4 4 2 2 0 0 15 20 25 15 20 25 Hand-spans Hand-spans (cm) (cm) Histogram Polygon
11. 11.  Curve The curve from polygon above would like this. 12 12 10 10 8 8 Frequency Frequency 6 6 density density 4 4 2 2 0 0 15 20 25 15 20 25 Hand-spans Hand-spans (cm) Polygon (cm) Curve
12. 12. CHAPTER 2  Mode The mode is most commonly occuring value or item of data. Look (s) the data below. The mode is a time 20 and Time t 0 ≤ t < 10 at Frequency 4 30 tseconds.7 10 ≤ < 20 20 ≤ t < 30 9 30 ≤ t < 40 6 1 40 ≤ t < 50 Frequency 5 2 9 50 ≤ t < 60 3 8 7 6 60 ≤ t < 70 2 5 4 4 70 ≤ t < 80 2 3 2 2 1 1 80 ≤ t < 90 1 0 0 90 ≤ t < 100 0 1 20 30 40 50 60 70 80 90 10 110 12 0 Times (s) 0 0 100 ≤ t < 2 110
13. 13.  Median The centre or middle item of the data is known as the median. Example. Determine the Median of data : 8, 15, 7, 10, 4, 3, 8, 6, 5, 7, 8 Solution. Placing the data in the order yield: 3, 4, 5, 6, 7, 7, 8, 8, 8, 10, 15 The middle item is the one which is equidistant from the extreme values. 8, 8, 10, 3, 4, 5, 6, 7 ,8, 7, 15 Media n
14. 14.  Cumulative frequency Cumulative frequency are represented in table and graph. Cumulative frequency 40 polygon Time t (s) Freque Cumulativ ncy e frequency Frequency cumulative 30 0 ≤ t < 10 4 4 10 ≤ t < 20 7 11 22 20 20 ≤ t < 30 9 20 30 ≤ t < 40 6 26 10 40 ≤ t < 50 5 31 50 ≤ t < 60 3 34 0 60 ≤ t < 120 9 43 10 20 30 40 50 60 70 80 90 100110120130 Upper class values Estimate of median (s)
15. 15.
16. 16. Look at the data from table below. Time (s) Frequency Time X Frequency 5 4 20 15 7 105 25 9 225 35 6 210 45 5 225 55 3 165 90 9 810 Total 43 1770