Statistics
Download as ppt, pdf1 like347 views
The document discusses frequency distributions and methods for organizing and presenting both quantitative and categorical data. It provides examples of constructing frequency distributions and histograms for quantitative data, including determining class intervals and boundaries. For categorical data, it demonstrates creating frequency tables and bar or pie charts to summarize ratings data. The goal is to condense raw data into more useful forms for analysis and visual interpretation.
More Related Content
Viewers also liked (20)
Similar to Statistics (20)
More from Zahida Pervaiz (20)
Recently uploaded (20)
Statistics
- 1. GOALS 1. Organize qualitative data into a frequency table. 2. Present a frequency table as a bar chart or a pie chart. 3. Organize quantitative data into a frequency distribution. 4. Present a frequency distribution for quantitative data using histograms, frequency polygons, and cumulative frequency polygons. Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-1
- 2. Tabulating Numerical Data: Frequency Distributions What is a Frequency Distribution? A frequency distribution is a list or a table … containing class groupings (ranges within which the data fall) ... and the corresponding frequencies with which data fall within each grouping or category Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-2
- 3. Why Use a Frequency Distribution? It is a way to summarize numerical data It condenses the raw data into a more useful form... It allows for a quick visual interpretation of the data Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-3
- 4. Class Intervals and Class Boundaries Each class grouping has the same width Determine the width of each interval by Width of interval @ range number of desired class groupings Usually at least 5 but no more than 15 groupings Class boundaries never overlap Round up the interval width to get desirable endpoints Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-4
- 5. EExxaammppllee:: HHoonnddaa AAuuttoo RReeppaaiirr TThhee mmaannaaggeerr ooff HHoonnddaa AAuuttoo wwoouulldd lliikkee ttoo hhaavvee aa bbeetttteerr uunnddeerrssttaannddiinngg ooff tthhee ccoosstt ooff ppaarrttss uusseedd iinn tthhee eennggiinnee ttuunnee--uuppss ppeerrffoorrmmeedd iinn tthhee sshhoopp.. SShhee eexxaammiinneess 5500 ccuussttoommeerr iinnvvooiicceess ffoorr ttuunnee--uuppss.. TThhee ccoossttss ooff ppaarrttss,, rroouunnddeedd ttoo tthhee nneeaarreesstt ddoollllaarr,, aarree lliisstteedd oonn tthhee nneexxtt sslliiddee.. Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-5
- 6. EExxaammppllee:: HHoonnddaa AAuuttoo RReeppaaiirr SSaammppllee ooff PPaarrttss CCoosstt ffoorr 5500 TTuunnee--uuppss 91 78 93 57 75 52 99 80 97 62 71 69 72 89 66 75 79 75 72 76 104 74 62 68 97 105 77 65 80 109 85 97 88 68 83 68 71 69 67 74 62 82 98 101 79 105 79 69 62 73 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-6
- 7. Tabular Summary: Frequency and Percent Frequency PPaarrttss CCoosstt (($$)) 5500--5599 6600--6699 7700--7799 8800--8899 9900--9999 110000--110099 PPaarrttss FFrreeqquueennccyy 22 1133 1166 77 77 55 5500 PPeerrcceenntt FFrreeqquueennccyy 44 2266 3322 1144 1144 1100 110000 ((22/5500))110000 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-7
- 8. Graphical Summary: Histogram 18 16 14 12 10 8 6 4 2 Parts Cost ($) Frequency 50-59 60-69 70-79 80-89 90-99 100-110 TTuunnee--uupp PPaarrttss CCoosstt Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-8
- 9. Histogram (Continued) Symmetric Left tail is the mirror image of the right tail Example: heights and weights of people Relative Frequency .35 .30 .25 .20 .15 .10 .05 0 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-9
- 10. Histogram (Continued) Moderately Skewed Left A longer tail to the left Example: exam scores Relative Frequency .35 .30 .25 .20 .15 .10 .05 0 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-10
- 11. Histogram (Continued) Moderately Right Skewed A Longer tail to the right Example: housing values Relative Frequency .35 .30 .25 .20 .15 .10 .05 0 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-11
- 12. Histogram (Continued) Highly Skewed Right A very long tail to the right Example: .35 executive salaries .30 Relative Frequency .05 .25 .20 .15 .10 0 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-12
- 13. Frequency Distribution Example Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-13
- 14. Frequency Distribution Example (continued) Sort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Find range: 58 - 12 = 46 Select number of classes: 5 (usually between 5 and 15) Compute class interval (width): 10 (46/5 then round up) Determine class boundaries (limits): 10, 20, 30, 40, 50, 60 Compute class midpoints: 15, 25, 35, 45, 55 Count observations assign to classes Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-14
- 15. Frequency Distribution Example Data in ordered array: (continued) 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Relative Frequency Percentage Class Frequency 10 but less than 20 3 .15 15 20 but less than 30 6 .30 30 30 but less than 40 5 .25 25 40 but less than 50 4 .20 20 50 but less than 60 2 .10 10 Total 20 1.00 100 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-15
- 16. Tabulating Numerical Data: Cumulative Frequency 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class Data in ordered array: Frequency Cumulative Percentage Cumulative Percentage Frequency 10 but less than 20 3 15 3 15 20 but less than 30 6 30 9 45 30 but less than 40 5 25 14 70 40 but less than 50 4 20 18 90 50 but less than 60 2 10 20 100 Total 20 100 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-16
- 17. Graphing Numerical Data: The Histogram A graph of the data in a frequency distribution is called a histogram The class boundaries (or class midpoints) are shown on the horizontal axis the vertical axis is either frequency, relative frequency, or percentage Bars of the appropriate heights are used to represent the number of observations within each class Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-17
- 18. Histogram Example Histogram: Daily High Temperature 7 6 5 4 3 2 1 0 5 15 25 35 45 55 65 Frequency Frequency Class Midpoints Class Midpoint 10 but less than 20 15 3 20 but less than 30 25 6 30 but less than 40 35 5 40 but less than 50 45 4 50 but less than 60 55 2 (No gaps between bars) Class Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-18
- 19. Graphing Numerical Data: The Frequency Polygon Frequency Polygon: Daily High Temperature 7 6 5 4 3 2 1 0 5 15 25 35 45 55 65 Frequency Class Midpoints Class Frequency Class Midpoint 10 but less than 20 15 3 20 but less than 30 25 6 30 but less than 40 35 5 40 but less than 50 45 4 50 but less than 60 55 2 (In a percentage polygon the vertical axis would be defined to show the percentage of observations per class) Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-19
- 20. Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon) Ogive: Daily High Temperature 100 80 60 40 20 0 10 20 30 40 50 60 Cumulative Percentage Class Boundaries (Not Midpoints) Class Cumulative Percentage Lower class boundary Less than 10 0 0 10 but less than 20 10 15 20 but less than 30 20 45 30 but less than 40 30 70 40 but less than 50 40 90 50 but less than 60 50 100 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-20
- 21. Categorical Data Categorical data involves categories or groups. These can be made without the fear of their order to be disturbed i.e. sex, age, marital status. It covers the following topics: Frequency Distribution Graphs Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-21
- 22. Example: Marada Inn Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are: BBeellooww AAvveerraaggee AAbboovvee AAvveerraaggee AAbboovvee AAvveerraaggee AAvveerraaggee AAbboovvee AAvveerraaggee AAvveerraaggee AAbboovvee AAvveerraaggee AAvveerraaggee AAbboovvee AAvveerraaggee BBeellooww AAvveerraaggee PPoooorr EExxcceelllleenntt AAbboovvee AAvveerraaggee AAvveerraaggee AAbboovvee AAvveerraaggee AAbboovvee AAvveerraaggee BBeellooww AAvveerraaggee PPoooorr AAbboovvee AAvveerraaggee AAvveerraaggee AAvveerraaggee Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-22
- 23. FFrreeqquueennccyy DDiissttrriibbuuttiioonn RRaattiinngg FFrreeqquueennccyy PPoooorr BBeellooww AAvveerraaggee AAvveerraaggee AAbboovvee AAvveerraaggee EExxcceelllleenntt 22 33 55 99 11 TToottaall 2200 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-23
- 24. BBaarr GGrraapphh 10 9 8 7 MMaarraaddaa IInnnn QQuuaalliittyy RRaattiinnggss Excellent Frequency Poor Below Average Average Above Average Rating 6 5 4 3 2 1 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-24
- 25. PPeerrcceennttaaggee FFrreeqquueennccyy DDiissttrriibbuuttiioonn RRaattiinngg PPeerrcceennttaaggeess PPoooorr BBeellooww AAvveerraaggee AAvveerraaggee AAbboovvee AAvveerraaggee EExxcceelllleenntt 1100 1155 2255 4455 55 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-25
- 26. PPiiee CChhaarrtt MMMMaaaarrrraaaaddddaaaa IIIInnnnnnnn QQQQuuuuaaaalllliiiittttyyyy RRRRaaaattttiiiinnnnggggssss Poor 10% Below Average 15% Average 25% Excellent 5% Above Average 45% Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-26
- 27. PPeerrcceennttaaggee FFrreeqquueennccyy DDiissttrriibbuuttiioonn RRaattiinngg AAnngglleess PPoooorr BBeellooww AAvveerraaggee AAvveerraaggee AAbboovvee AAvveerraaggee EExxcceelllleenntt 3366 5544 9900 116622 1188 CCuummiillaattiivvee AAnngglleess 3366 9900 118800 334422 336600 Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-27