1. CHAPTER 5 Basic Statistics
Data Summary and Presentation:
Types of Data
Graphical Data Presentation
Numerical Data Presentation

2. Statistic in Engineering
Statistics is science of data; the art of conducting studies or experiments through collecting, organizing, summarizing and analyzing data before some conclusion are drawn.

3. DESCRIPTIVE STATISTICS INFERENTIAL STATISTICS
Present quantitative description in manageable form.
Graphical representatives and numerical analysis.
To make inferences from sample data to reflect the population.
Also called inductive reasoning or inductive statistics.
Using a sample to draw conclusions about a population

4. Basic Terms in Statistics
Population
Entire collection of individuals which are characteristic being studied.
Sample
A portion, or part of the population interest (a group of subjects selected from a population).
Variable
Characteristics of the individuals within the population.
Observation
Value of variable for an element.
Data Set
- A collection of observation on one or more variables.
Name
Score
Mohd Amirul bin Hamdi 90
Variable
Element
Observation/ Measurement

6. Standard error of proportion
Characteristic
Population
Sample
Statistical measure
Parameter
Statistic
Size N n
Mean
Variance
Standard deviation
Proportion
Standard error of mean
Standard error of proportion

7. Data Summary & Presentation

8. Types of Data: Qualitative & Quantitative Data
Deals with numbers.
Data which can be measured.
Describe by quantity.
There are two types of quantitative data:-
i. Discrete Data
Items or values are countable, can assume only certain values with no intermediate values. The possible values may be fixed (finite) to infinity.
ii. Continuous Data
Measurements and possible values cannot be counted and can be described using interval on real number line.

9. Types of Data: Qualitative & Quantitative Data
2) Qualitative Data
Deals with descriptions.
Can be observed but not measured.
Cannot be assume in a numerical value but can be classified into two or more nonnumeric categories.
Describe by quality.

10. TYPES OF DATA Quantitative Qualitative Discrete
(e.g, number of houses, cars accidents
Continuous (e.g., length, age, height, weight, time)
e.g., gender, marital status
Qualitative

11. (can be in quantitative)
Measurement Levels and the Appropriate Averages
ALL DATA
Qualitative data
Quantitative data
Nominal
Car makes,
Days of Week,
Gender
Ordinal
(can be in quantitative)
TV channel
Ranks and title
Calendar dates
Interval and Ratio
Sales ($)
Accounts Receivable
Market share
Mode
Median
Mean

12. Grouped Data Vs Ungrouped Data
Grouped data - Data that has been organized into groups (into a frequency distribution).
Ungrouped data - Data that has not been organized into groups. Also called as raw data.

13. Graphical Data Presentation

14. Graphical Data Presentation
Data can be summarized or presented in two ways:
1. Tabular
2. Charts/graphs.
The presentations usually depends on the type (nature) of data whether the data is in qualitative (such as gender and ethnic group) or quantitative (such as income and CGPA).

15. Data Presentation of Qualitative Data
Tabular presentation for qualitative data is usually in the form of frequency table that is a table represents the number of times the observation occurs in the data.
*Qualitative :- characteristic being studied is nonnumeric. Examples:- gender, religious affiliation or eye color.
The most popular charts for qualitative data are:
1. bar chart/column chart;
2. pie chart; and
3. line chart.

16. Types of Graph Qualitative Data

17. Example 5.1.1: Frequency Table
Bar Chart: used to display the frequency distribution in the graphical form.
Example 5.1.2:
Observation
Frequency
Malay 33
Chinese 9
Indian 6
Others 2

18. Pie Chart: used to display the frequency distribution
Pie Chart: used to display the frequency distribution. It displays the ratio of the observations
Example :
Line chart: used to display the trend of observations. It is a very popular display for the data which represent time.
Example 5.1.4
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec 10 7 5 39
260
316
142 11 4 9

19. Data Presentation Of Quantitative Data
Tabular presentation for quantitative data is usually
in the form of frequency distribution that is a
table represent the frequency of the observation
that fall inside some specific classes (intervals).
*Quantitative : variable studied are numerically. Examples:-
balanced in accounts, ages of students, the life of an
automobiles batteries such as 42 months).
Frequency distribution: A grouping of data into mutually
exclusive classes showing the number of observations in
each class.

20. There are few graphs available for the
graphical presentation of the quantitative data.
The most popular graphs are:
1. Frequency distribution and histogram;
2. frequency polygon
3. Ogive.
4. Stem-and-Leaf plot
5. Box plot.

21. Weight (Rounded decimal point)
Example 5.1.5: Frequency Distribution
Histogram: Looks like the bar chart except that the horizontal axis represent the data which is quantitative in nature. There is no gap between the bars.
Example 5.1.6:
Weight (Rounded decimal point)
Frequency
60-62 5
63-65 18
66-68 42
69-71 27
72-74 8

22. HOW TO CONSTRUCT HISTOGRAM
Prepare the frequency distribution table by:
Find the minimum and maximum value.
Decide the number of classes to be included in your frequency distribution table.
Usually 5-20 classes. Too small – may not able to see any pattern. OR
Sturge’s rule: Number of classes =
Determine class width, i=(max-min)/num. of class.
Determine class limit. Use smallest value for the lower limit of first class.
Find class boundaries and class mid points.
Count frequency for each class.
Draw histogram.

23. Frequency Polygon: looks like the line chart except that the horizontal axis represent the class mark of the data which is quantitative in nature.
Example :
Ogive: line graph with the horizontal axis represent the upper limit of the class interval while the vertical axis represent the cummulative frequencies.
Example :

24. Stem-and-Leaf Plot : visual way to display a set of data usually large data set
Example :
Box Plot
Example :
STEM
LEAF 1 2
1 3
Distribution data:
skewed to the right with a short tail

25. Numerical Data Presentation
Measures of Central Tendency
Measures of Dispersion
Measures of Position

26. Data Summary
Summary statistics are used to summarize a set of observations.
Two basic summary statistics are measures of central tendency and measures of dispersion.
Measures of Central Tendency
Mean
Median
Mode
Measures of Dispersion
Range
Variance
Standard deviation
Measures of Position
Z scores
Percentiles
Quartiles
Outliers
Measures of average are also called measures of
central tendency and include the mean, median, mode, and midrange.
How the data values are dispersed, do the data values cluster around the mean, or are they spread more evenly throughout the distribution? The measures that determine the spread of the data values are called measures of variation, or measures of dispersion.
Tell where a specific data value falls within the data set or its relative position in comparison with other data values.

27. Measures of Central Tendency
Mean
Mean of a sample is the sum of the sample data divided by the total number sample.
Mean for ungrouped data is given by:
Mean for group data is given by:

28. Example 5.1.11 (Ungrouped data): Mean for the sets of data 3,5,2,6,5,9,5,2,8,6 Solution :

29. Example (Grouped Data): Use the frequency distribution of weights 100 male students in XYZ university, to find the mean.
Weight
Frequency
60-62
63-65
66-68
69-71
72-74 5 18 42 27 8

30. Weight (Class Interval
Solution :
Weight (Class Interval
Frequency, f
Class Mark, x fx
60-62
63-65
66-68
69-71
72-74 5 18 42 27 8

31. Median of ungrouped data: The median depends on the
number of observations in the data, n . If n is odd, then the
median is the (n+1)/2 th observation of the ordered observations.
But if is even, then the median is the arithmetic mean of the
n/2 th observation and the (n+1)/2 th observation.
Median of grouped data:

32. Averages (The Median) Single middle value Ordered data
The median is the middle value of a set of data once the data has been ordered.
Example Ali hit 11 balls in a golf tournament. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives.
85, 125, 130, 65, 100, 70, 75, 50, 140, 95, 70
50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 140
Ordered data
Single middle value
Median drives = 85 yards

33. Two middle values so take the mean.
Averages (The Median)
The median is the middle value of a set of data once the data has been ordered.
Example Ali hit 12 balls at golf tournament. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives.
85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70
50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140
Ordered data
Two middle values so take the mean.
Median drive = 90 yards

34. Weight (Class Interval Cumulative Frequency, F
Example (Grouped Data): The sample median for frequency distribution as in example Solution:
Weight (Class Interval
Frequency, f
Class Mark, x fx
Cumulative Frequency, F
Class Boundary
60-62
63-65
66-68
69-71
72-74 5 18 42 27 8 61 64 67 70 73
305
1152
2814
1890
584

35. Mode Mode of ungrouped data: The value with the highest frequency in a data set *It is important to note that there can be more than one mode and if no number occurs more than once in the set, then there is no mode for that set of numbers

36. Mode for grouped data

37. Weight (Class Interval Cumulative Frequency, F
Example (Ungrouped data) Find the mode for the sets of data 3, 5, 2, 6, 5, 9, 5, 2, 8, 6 Mode = number occurring most frequently = 5 Example Find the mode of the sample data below Solution:
Weight (Class Interval
Frequency, f
Class Mark, x fx
Cumulative Frequency, F
Class Boundary
60-62
63-65
66-68
69-71
72-74 5 18 42 27 8 61 64 67 70 73
305
1152
2814
1890
584 23 65 92
100
Total
6745
Mode class

38. Measures of Dispersion
Range = Largest value – smallest value
Variance: measures the variability (differences) existing in a set of data.
The variance for the ungrouped data:
The standard deviation for the ungrouped data:

39. Measures of Dispersion
The variance for the grouped data:
The standard deviation for the grouped data:

40. A large variance means that the individual scores (data) of the sample deviate a lot from the mean.
A small variance indicates the scores (data) deviate little from the mean.

41. Example 5.1.18 (Ungrouped data)
Find the variance and standard deviation of the sample data :
3, 5, 2, 6, 5, 9, 5, 2, 8, 6

42. Weight (Class Interval Cumulative Frequency, F
Example (Grouped data) Find the variance and standard deviation of the sample data below:
Weight (Class Interval
Frequency, f
Class Mark, x fx
Cumulative Frequency, F
Class Boundary
60-62
63-65
66-68
69-71
72-74 5 18 42 27 8 61 64 67 70 73
305
1152
2814
1890
584 23 65 92
100
Total
6745

43. Weight (Class Interval Cumulative Frequency, F
Example (Grouped data)
Find the variance and standard deviation of the sample data below:
Weight (Class Interval
Frequency, f
Class Mark, x
Cumulative Frequency, F
Class Boundary fx x2
fx2
60-62
63-65
66-68
69-71
72-74 5 18 42 27 8 61 64 67 70 73 23 65 92
100
305
1152
2814
1890
584
3721
4096
4489
4900
5329
18605
73728
188538
132300
42632
Total
6745
455803