Statistic chapter 1 & 2

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Statistic chapter 1 & 2

  1. 1. STATISTIC
  2. 2. Outline1. HISTOGRAM  Histogram Frequency Density Polygon and Curve  Polygon  Curve2. CHAPTER 2  Mode  Median  Cumulative frequency  Mean
  3. 3. HISTOGRAMA 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 ina 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. SolutionThe first step is to calculate the width of each of theclasses. The first class is of width 0.5, the next ofwidth 1.0 and so on.The result of these two steps are recorded in theexpanded table below. Class width Class Frequency Frequency density0 ≤ x < 0.5 12 0.5 12:5 = 240.5 ≤ x < 32 1 321.51.5 ≤ x < 20 1 202.52.5 ≤ x < 20 2 104.54.5 ≤ x < 6 2 36.5
  9. 9.  4 0 3 0Frequency 2density 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 8Frequency Frequency 6 6density 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 8Frequency Frequency 6 6density 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 ModeThe mode is most commonly occuring value oritem of data.Look (s) the data below. The mode is a time 20 and Time t 0 ≤ t < 10 at Frequency 430 tseconds.7 10 ≤ < 2020 ≤ t < 30 930 ≤ t < 40 6 140 ≤ t < 50 Frequency 5 2 950 ≤ t < 60 3 8 7 660 ≤ t < 70 2 5 4 470 ≤ t < 80 2 3 2 2 1 180 ≤ t < 90 1 0 090 ≤ t < 100 0 1 20 30 40 50 60 70 80 90 10 110 12 0 Times (s) 0 0100 ≤ t < 2110
  13. 13.  MedianThe centre or middle item of the data is known asthe median.Example. Determine the Median of data : 8, 15, 7, 10, 4, 3, 8, 6, 5, 7, 8Solution. Placing the data in the order yield: 3, 4, 5, 6, 7, 7, 8, 8, 8, 10, 15The middle item is the one which is equidistantfrom 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 300 ≤ t < 10 4 410 ≤ t < 20 7 11 22 2020 ≤ t < 30 9 2030 ≤ t < 40 6 26 1040 ≤ t < 50 5 3150 ≤ t < 60 3 34 060 ≤ 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

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