1. BUSINESS MATHEMATICS
&
STATISTICS

2. Statistical Representation Measures of Central Tendency
LECTURE 24
Statistical Representation Measures of Central Tendency
Part 1

3. LINE GRAPHS
Causes of death

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

5. Affected by extreme values
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
and 74 (8 marks).
Sum = 596
Mean = 596/8 = 74.5
Affected by extreme values

6. data are arranged in order.
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
The median is the middle score, or the mean of the two middle scores, when the scores are placed in order

7. 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
The mode, or most common value, is 1.

8. 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

9. 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

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

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

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

13. Tabulating Numerical Data: Frequency Distributions
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
= 46
Select Number of Classes
5 (usually between 5 and 15)

14. 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

15. TABULATING NUMERICAL DATA FREQUENCY DISTRIBUTIONS
Data in ordered array
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 under
20 but under
30 but under
40 but under
50 but under
Total

16. BUSINESS MATHEMATICS
&
STATISTICS

17. BUSINESS MATHEMATICS
&
STATISTICS

18. BUSINESS MATHEMATICS
&
STATISTICS