1. Chapter 5
STATISTICS (PART 1)

2. What is statistics? Numerical facts
The science of learning from data.
Numerical facts
Collection of methods for planning experiments, obtaining data and organizing, analyzing, interpreting and drawing the conclusions or making a decision

3. Basic Terms in Statistics
Population: A collection, or set, of individuals or objects or events whose properties are to be analyzed.
Sample: A subset of the population.
Element: Entities on which data are collected.
Observation: Value of variable for an element.
Data Set: A collection of observation on one or more variables.
Population
Sample

4. Grouped Data Vs Ungrouped Data
Ungrouped data – Data that has not been organized into groups. Also called as raw data.
Grouped data - Data that has been organized into groups (into a frequency distribution).
Data
Frequency 2 8 3 4 5 6 7 9
Data
Frequency
2 – 4 5
5 – 7 6
8 – 10 10
11 – 13 8
14 – 16 4
17 – 19 3

5. Data type VARIABLES QUALITATIVE NOMINAL Example: gender, color ORDINAL
Example: Pass/Fail, Good, Bad
QUANTITATIVE
DISCRETE
Example:
Counts- number of items/integers
CONTINUOUS
Example: Measurement- Length, weight

6. Example 6.1
Identify each of the following examples as qualitative or quantitative variables.
1. The residence hall for each student in a statistics
class. (qualitative)
2. The amount of gasoline pumped by the next 10 customers
at the local Unimart. (quantitative )
3. The amount of radon in the basement of each of 25 homes
in a new development. (quantitative )
4. The color of the baseball cap worn by each of 20
students. (qualitative)
5. The length of time to complete a mathematics
homework assignment. (quantitative )
6. The state in which each truck is registered when
stopped and inspected at a weigh station. (qualitative

7. Discrete & coNTINUOUS
Discrete data is data which can only take certain values, or can be counted. The number of people in a room can only be 1, 2, 3, … and not 1.23, 1.57, Example:
- Number of car on a road
- Number of children in a family
Continuous data cannot assume exact values but can assume any values between two given values. The data is acquired through the process of measuring. For example, the height 175 cm (correct to the nearest cm) could have arisen from any values in the range.
- Weight of people
- Speeds of motor boats at a particular part of a race
- The times taken by each of student to run 100m

8. STATISTICS Descriptive Inferential
Provide simple summaries about the sample and the measures
Trying to reach conclusion that extend beyond the immediate data alone
STATISTICS
Descriptive
Inferential
- Measurement of central tendency
- Measurement of dispersion
Confidence Interval
Hypothesis testing

9. Descriptive Statistics
A study on data summary or describes a collection, data organization (presentation of data in a more informative way such as graphical, diagrams and charts).
In general divided by two categories :-
- Data presentation (display)
- Tabular
- Charts/graphs

10. Inferential Statistics
Branch of statistics: using a sample to draw conclusions about a population (basic tool: probability).
Consists of generalizing from samples to population, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.
Area statistics which are deal with decision making procedures.
Population – consists of all subjects (human or otherwise) that are being studied.
Sample – is a group of subjects selected from a population.

11. Weight of 100 male students in XYZ university
Constructing Frequency Distribution
When summarizing large quantities of raw data, it is often
useful to distribute the data into classes.
A frequency distribution for quantitative data lists all the
classes and the number of values that belong to each class.
Weight
Frequency
60-62 5
63-65 18
66-68 42
69-71 27
72-74 8
Total
100
Weight of 100 male students in XYZ university

12. Table 6.1: Weight of 100 male students in XYZ university
For quantitative data, an interval that includes all the values that fall within two numbers; the lower and upper class which is called class.
Class is in first column for frequency distribution table.
*Classes always represent a variable, non-overlapping; each value is belong to one and only one class.
The numbers listed in second column are called frequencies, which gives the number of values that belong to different classes. Frequencies denoted by f.
Table 6.1: Weight of 100 male students in XYZ university
Variable
Weight
Frequency
60-62 5
63-65 18
66-68 42
69-71 27
72-74 8
Total
100
Frequency
column
Frequency
of the third
class.
Third class
(Interval Class)

13. The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class.
The difference between the two boundaries of a class gives
the class width; also called class size.
Formula:
- Class Midpoint or Mark
Class midpoint or mark = (Lower Limit + Upper Limit)/2
- Class Width / Class Size
class width , c =Upper Limit– Lower Limit

14. Cumulative Frequency Distributions
A cumulative frequency distribution gives the total number of values that fall below the upper boundary of each class.
In cumulative frequency distribution table, each class has the same lower limit but a different upper limit.
Table 6.2: Class Limit, Class Boundaries, Class Width , Cumulative Frequency
Weight
(Class Interval)
Number of Students, f
Class Boundaries
Cumulative Frequency
60-62 5
63-65 18
= 23
66-68 42
= 65
69-71 27
=92
72-74 8
= 100
TOTAL
100

15. Example 6.9: From Table 6.1: Class Boundary
Weight
(Class Interval)
Class Boundary
Frequency
60-62 5
63-65 18
66-68 42
69-71 27
72-74 8
Total
100

16. Data summary - Variance - Standard deviation
Measures of Central Tendency
- Mean
- Median
- Mode
Measures of Dispersion
- Variance
- Standard deviation
Measures of average are also called measures of
central tendency and include the mean, median, mode, and midrange.
After know about average, you must know how the data values are dispersed. That is, do the data values cluster around the mean.

17. Measures of Central Tendency
Mean
Mean of a sample is the sum of the sample data divided by the total number sample.
GROUPED DATA:
When the data has been grouped into intervals and the mid-points of the intervals are denoted by

18. Exercise 6.2:
Consider data set of weights of 30 students. Find the mean of grouped data.
Answer: 46.5 kg
Weight(kg)
Frequency (f)
20-29 1
30-39 8
40-49 10
50-59 6
60-69 5

19. Median
The median is the middle value of a set of numbers arranged in order of magnitude and normally is denoted by,
GROUPED DATA:
The median of frequency distribution data can be described as:

20. Exercise 6.3: Find the median of the following data: 1. Answer: 15.52.
Answer: 11
Class
Frequency
1-5
6-10
11-15
16-20
21-25
26-30 2 4 9 7 5 3
Total 30
Class interval
1 – 3
4 – 6
7 – 9
10 – 12
13 – 15
16 – 18
Frequency 5 3 2 1 6 4

21. Mode
The mode of a set of numbers is the value which occurs most often and denoted by ,
GROUPED DATA:
The median of frequency distribution data can be described as:
NOTE: Class with the highest frequency is called MODAL CLASS

22. Exercise 6.4: Find the mode of the following data: 1. Answer: 14.07 2.
Class
Frequency
1-5
6-10
11-15
16-20
21-25
26-30 2 4 9 7 5 3
Total 30
Class interval
1 – 3
4 – 6
7 – 9
10 – 12
13 – 15
16 – 18
Frequency 5 3 2 1 6 4

23. relationships between the measurements
When the mean, median and mode are all equal, the distribution of the data set has a bell-shaped curve. The distribution is then said to be symmetric.
If Mode < Median < Mean, then the distribution is said to be positive/right skewed, meaning there are a few unusual large values.
If Mean < Median < Mode, then the distribution is said to be negative/left skewed, that is there are some unusual small values.

24. Measures of Dispersion
The standard deviation from the mean is used widely in statistics to indicate the measure of dispersion. Small standard deviation tells that most of the data is close to the mean. While large standard deviation shows that much of the data is far from the mean.

25. Variance & standard deviation
GROUPED DATA:

26. Weight (Class Interval) Cumulative Frequency, F
Example 6.10 (Grouped data) Find the variance and standard deviation of the sample data below: Answer : s2=8.61;s=2.93
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

27. Exercise 6.45:
Consider data set of weights of 30 students. Find the standard
deviation.
Answer:
Weight(kg)
Frequency (f)
20-29 1
30-39 8
40-49 10
50-59 6
60-69 5