BUSINESS MATHEMATICS STATISTICS LECTURE 24 Statistical Representation Measures

BUSINESS MATHEMATICS & STATISTICS

LECTURE 24 Statistical Representation Measures of Central Tendency Part 1

LINE GRAPHS Causes of death

LINE GRAPHS Temperature of cities A, B, C and D

MEAN The most common average is the mean. The mean is used for things like marks and scores (e. g. sport), and is found by adding all the scores and dividing by the number of scores. Marks 58 69 73 67 76 88 91 and 74 (8 marks). Sum = 596 Mean = 596/8 = 74. 5 Affected by extreme values

MEDIAN Another typical value is the median. The median is the middle value when the data are arranged in order. The median is easier to find than the mean, and unlike the mean it is not affected by values that are unusually high or low 3 6 11 14 19 19 21 24 31 The median is the middle score, or the mean of the two middle scores, when the scores are placed in order

MODE The most common score in a set of scores is called the mode. There may be more than one mode, or no mode at all 2212032114111220321 The mode, or most common value, is 1.

ORGANISING DATA Organising Numerical Data The Ordered Array and Stem-leaf Display Tabulating and Graphing Numerical Data Frequency Distributions: Tables, Histograms, Polygons Cumulative Distributions: Tables, the Ogive

ORGANISING DATA Tabulating and Graphing Univariate Categorical Data The Summary Table Bar and Pie Charts, the Pareto Diagram Tabulating and Graphing Bivariate Categorical Data Contingency Tables Side by Side Bar charts Graphical Excellence and Common Errors in Presenting Data

Organizing Numerical Data Ordered Array 21, 24, 26, 27, 30, 32, 38, 41 Stem and Leaf Display 2 144677 3 028 4 1 41, 24, 32, 26, 27, 30, 24, 38, 21 Frequency Distributions Cumulative Distributions Histograms Tables Ogive Polygons

ORGANISING NUMERICAL DATA Data in Raw form (as collected) 24, 26, 24, 21, 27, 30, 41, 32, 38 Data Ordered from Smallest to Largest: 21, 24, 26, 27, 30, 32, 38, 41 Stem and Leaf display: 2 144677 3 028 4 1

Tabulating and Graphing Numerical Data Ordered Array 21, 24, 26, 27, 30, 32, 38, 41 Stem and Leaf Display 2 144677 3 028 4 1 41, 24, 32, 26, 27, 30, 24, 38, 21 Frequency Distributions Cumulative Distributions Histograms Tables Ogive Polygons

Tabulating Numerical Data: Frequency Distributions Sort Raw Data in Ascending Order 12, 13, 17, 21, 24, 26, 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)

Tabulating Numerical Data: Frequency Distributions Compute Class Interval (width) 10 (46/5 then round up) Determine Class Boundaries (limits) 10, 20, 30, 40, 50 Compute Class Midpoints 15, 25, 35, 45, 55 Count Observations & Assign to Classes

TABULATING NUMERICAL DATA FREQUENCY DISTRIBUTIONS Data in ordered array 12, 13, 17, 21, 24, 26, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class 10 but under 20 20 but under 30 30 but under 40 40 but under 50 50 but under 60 Total Frequency 3 6 5 4 2 20 Relative Percentage Frequency. 15. 30. 25. 20. 10 1 15 30 25 20 10 100

BUSINESS MATHEMATICS & STATISTICS