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# Statistics lecture 3 (ch2)

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Lecture 3

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### Statistics lecture 3 (ch2)

1. 1. 1
2. 2. • Need to gain information from data.• Data must be organised and reduced.• Descriptive statistics – Organising data into tables, charts and graphs. – Numerical calculations.• Single variable data• Raw data – Collected data before it is grouped or ranked. 2
3. 3. Organising and graphing qualitative data in afrequency distribution table.Example:The data below shows the gender of 50 employees and thedepartment in which they work at ABC Ltd. HR – Human resources Emp. no. Gender Dept. Emp. no. ….. Gender Mark. – Marketing Dept 1 M HR 6 M Fin. – Finance Fin. ….. M – Male 2 F Mark. 7 M Mark. ….. F – Female 3 M Fin. 8 M Fin. ….. 4 F HR 9 F HR ….. 5 F Fin. 10 F Fin. ….. 3
4. 4. HR Marketing Finance M │ │ │││ F ││ │ ││Emp. no. Gender Dept. Emp. no. Gender Dept ….. 1 M HR 6 M Fin. ….. 2 F Mark. 7 M Mark. ….. 3 M Fin. 8 M Fin. ….. 4 F HR 9 F HR ….. 5 F Fin. 10 F Fin. ….. 4
5. 5. Organising and graphing qualitative data in a frequencydistribution table. HR Marketing Finance M 4 10 5 F 10 16 5 5
6. 6. Organising and graphing qualitative data in a frequencydistribution table. HR Marketing Finance Total M 4 10 5 19 F 10 16 5 31 Total 14 26 10 50 6
7. 7. Pie charts HR Mark Fin Total Total 14 26 10 50 14/50×360 26/50×360 10/50×360 Degrees 360 = 101 = 187 = 72 14/50×100 26/50×100 10/50×100Percentage 100 = 28 = 52 = 20 Employees at ABC 20% 28% Human resources Marketing Finance 52% 7
8. 8. Pie charts Male Female Total Total 19 31 50 19/50×360 31/50×360 Degrees 360 = 137 = 223 19/50×100 31/50×100Percentage 100 = 38 = 62 Employees at ABC 38% Male Female 62% 8
9. 9. Bar graphs HR Marketing Finance Total M 4 10 5 19 F 10 16 5 31 Total 14 26 10 50 Employees at ABC Employees at ABC 30 26 35 Number of workers 31 25 Number of workers 30 20 25 14 19 15 10 20 10 15 5 10 0 5 Human Marketing Finance 0 resources Male Female 9
10. 10. Multiple bar graphs HR Marketing Finance Total M 4 10 5 19 F 10 16 5 31 Total 14 26 10 50 Employees at ABC Employees at ABC Human 20 Number of workers 20 resourcesNumber of workers 15 Male 15 Marketing 10 10 Female 5 Finance 0 5 Human Marketing Finance 0 resources Male Female 10
11. 11. Stacked bar graphs HR Marketing Finance Total M 4 10 5 19 F 10 16 5 31 Total 14 26 10 50 Employees at ABC Employees at ABC Number of workers 35 Finance 30 25Number of workers 30 Female 20 25 15 Marketing 20 10 Male 15 5 10 0 Human 5 resources Human Marketing Finance 0 resources 11 Male Female
12. 12. DefinitionsFrequency Distribution– for qualitative data displays the possible categoriesalong with the number of times (or frequency) eachcategory appears in the data set.- for quantitative data is a summary of numerical dataprepared by dividing raw data into several non-overlapping class intervals and then counting howmany observations (frequency) of the variable fall intoeach classRelative Frequency – for a particular category is theportion or % of the observations within a category 12
13. 13. Organising and graphing quantitative data in a frequencydistribution table.• Frequency table consists of a number of classes and each observation is counted and recorded as the frequency of the class.• If n observations need to be classified into a frequency table, determine: – Number of classes: c  1  3,3log n xmax  xmin – Class width  c 13
14. 14. Organising and graphing quantitative data in a frequencydistribution table.Example:The following data represents the number of telephone callsreceived for two days at a municipal call centre. The data wasmeasured per hour. 8 11 12 20 18 10 14 18 16 9 5 7 11 12 15 14 16 9 17 11 6 18 9 15 13 12 11 6 10 8 11 13 22 11 11 14 11 10 9 19 14 17 9 3 3 16 8 2 14
15. 15. Frequency distributionNumber of classes  1  3,3log n  1  3,3log 48  6,5  7 xmax  xmin 22  2Class width    2,86  3 k 7 8 11 12 20 18 10 14 18 16 9 5 7 11 12 15 14 16 9 17 11 6 18 9 15 13 12 11 6 10 8 11 13 22 11 11 14 11 10 9 19 14 17 9 3 3 16 8 2 15
16. 16. Frequency distribution– first class [ xmin; ; min) class width) 2 5)32x– second class [ 5 ;; 8  3 ) width) 5 5 5 ) class“[“ value is included in class 8 11 12 20 18 10 14 18 16 9 5 7 11 12 15 14 16 9 17 11 6 18 9 15 13 12 11 6 10 8“)“ value is excluded from class 11 13 22 11 11 14 11 10 9 19 14 17 9 3 3 16 8 2 16
17. 17. Frequency distribution Classes Count [2;5) │││ 3 8 11 12 20 …. [5;8) |││││ | 4 5 7 11 12 …. [8;11) |│││││││││││ 11 6 18 9 15 …. [11;14) |│││││││││││││ | 13 11 13 22 11 …. [14;17) │││││││││ 9 19 14 17 9 …. [17;20) |││││││ 6 [20;23) ││ 2 17
18. 18. Frequency distribution Classes Frequency (f)[2;5) 3[5;8) 4[8;11) 11[11;14) 13[14;17) 9[17;20) 6[20;23) 2 Total 48 18
19. 19. Frequency distribution Classes f % frequency[2;5) 3 3/48×100 = 6,3[5;8) 4 4/48×100 = 8,3[8;11) 11 11/48×100 = 22,9[11;14) 13 27,1[14;17) 9 18,8[17;20) 6 12,5[20;23) 2 4,2 Total 48 100 19
20. 20. Frequency distributionClasses f %f Cumulative frequency (F)[2;5) 3 6,3 3[5;8) 4 8,3 3+4=7[8;11) 11 22,9 7 + 11 = 18[11;14) 13 27,1 18 + 13 = 31[14;17) 9 18,8 31 + 9 = 40[17;20) 6 12,5 40 + 6 = 46[20;23) 2 4,2 46 + 2 = 48 Total 48 100 20
21. 21. Frequency distribution Classes f %f F %F[2;5) 3 6,3 3 3/48×100 = 6,3[5;8) 4 8,3 7 7/48×100 = 14,6[8;11) 11 22,9 18 18/48×100 = 37,5[11;14) 13 27,1 31 64,6[14;17) 9 18,8 40 83,3[17;20) 6 12,5 46 95,8[20;23) 2 4,2 48 100 Total 48 100 21
22. 22. Frequency distribution Classes f F Class mid-points (x)[2;5) 3 3 (2 + 5)/2 = 3,5[5;8) 4 7 (5 + 8)/2 = 6,5[8;11) 11 18 (8 + 11)/2 = 9,5[11;14) 13 31 (11 + 14)/2 = 12,5[14;17) 9 40 15,5[17;20) 6 46 18,5[20;23) 2 48 21,5 Total 48 22
23. 23. Frequency distribution Classes f %f F %F (x)[2;5) 3 6,3 3 6,3 3,5[5;8) 4 8,3 7 14,6 6,5[8;11) 11 22,9 18 37,5 9,5[11;14) 13 27,1 31 64,6 12,5[14;17) 9 18,8 40 83,3 15,5[17;20) 6 12,5 46 95,8 18,5[20;23) 2 4,2 48 100 21,5 Total 48 100 23
24. 24. Histograms Classes f %f[2;5) 3 6,3[5;8) 4 8,3[8;11) 11 22,9 y-axis[11;14) 13 27,1[14;17) 9 18,8[17;20) 6 12,5[20;23) 2 4,2 x-axis 24
25. 25. Histograms Number of telephone calls per hour at a municipal call centre 14 Number of hours 12 10 8 6 4 2 0 2 5 8 11 14 17 20 23 Number of calls 25
26. 26. DefinitionsFrequency PolygonA line graph of a frequency distribution and offersa useful alternative to a histogram. Frequencypolygon is useful in conveying the shape of thedistributionOgiveA graphic representation of the cumulativefrequency distribution. Used for approximating thenumber of values less than or equal to a specifiedvalue 26
27. 27. Frequency polygonsClass mid-points (x) f %f 3,5 3 6,3 6,5 4 8,3 9,5 11 22,9 y-axis 12,5 13 27,1 15,5 9 18,8 18,5 6 12,5 21,5 2 4,2 x-axis 27
28. 28. Frequency polygons Number of telephone calls per hour at a municipal call centre (x) 14 3,5 Number of hours 12 6,5 10 8 9,5 6 12,5 4 2 15,5 0 18,5 0.5 3.5 6.5 9.5 12.5 15.5 18.5 21.5 24.5 21,5 Arbitrary mid-points to Number of calls 28 close the polygon.
29. 29. Ogives Classes F %F[2;5) 3 6,3[5;8) 7 14,6[8;11) 18 37,5 y-axis[11;14) 31 64,6[14;17) 40 83,3[17;20) 46 95,8[20;23) 48 100 x-axis 29
30. 30. Ogives Ogive of number of call received at a call centre per hour 100 number of hours 90 % Cumulative 80 70 60 50 40 30 20 10 0 2 5 8 11 14 17 20 23 Number of calls None of the hours had less than 2 calls. 30
31. 31. Ogives Ogive of number of call received20% of thehours had at a call centre per hourmore than 17 calls 100 number of hours 90 % Cumulative 80 per hour. 7080% of the 60hours had 50 less than 40 30 17 calls 20 10 0per hour. 2 5 8 11 14 17 20 23 50% of Number ofhad less the hours calls than 12 calls per hour. 31
32. 32. • Activity 1 Module Manual p 67• Activity 2 Module Manual p 68• Activity 3 Module Manual p 69• Revision Exercise 1 Module Manual p 70• Revision Exercise 2 Module Manual p 70 32
33. 33. • Revision Exercise 3 Module Manual p 71• Revision Exercise 4 Module Manual p 72• Concept Questions 1 -11 p 52 Elementary Statistics• Self Review Test p53 Elementary Statistics• Supplementary Exercises p 54 -59 Elementary Statistics 33