SOUTHWESTERN UNIVERSITY, NIGERIA
STA 111 – ELEMENTARY STATISTICS
Lecture Note by DANIEL Deborah O.
COURSE OUTLINE
Frequency Distribution- Class Interval, Class Limits, Class Boundaries, Data Presentation, Bar
Chart, Histogram, Cumulative Frequencies And O-Give;
Measure of Location or Central Tendency – Mean, Median, Mode, Quartiles and Percentiles for
Ungrouped and Grouped Data;
Measure of Dispersion – Range, Standard Deviation, Variance, Moment, Skewness and Kurtosis;
Probability Theory – Basic Laws of Probability, Addition of Probabilities, Conditional
Probability;
Probability Distribution – Binomial Distributions, Poisson Distribution and Normal Distribution.
,FREQUENCY DISTRIBUTIONS
Classification or grouping of data into a set of classes reflecting the pattern of occurrences is
referred to as frequency distribution. The following examples illustrate the construction of
frequency distribution
(1) 1 5 3 4 1 3 2 5
1 4 1 3 2 0 1 2
1 2 0 2 1 4 5 3
Solution
Let 𝑥 represent these data values, we can use a frequency distribution to represent this set of data
by listing the x values with their frequencies in the table below
𝑥 0 1 2 3 4 5
𝐹 2 6 6 4 3 3
(1) The genotype of a group of 25 babies treated for jaundice at a public health centre are
as follows; AA AA AS AS AA AS AA AA SS AA SS AS AA AA AS AS
SS AA AS AS, AA, AA, SS, AS, AS
Solution
Genotype Number of babies
AA 11
AS 10
SS 4
Total 25
(3) The dry weights in mg of 30 seedlings of a pawpaw variety at germination are as
follows;
10.6 11.6 13.0 12.1 14.6 15.9 14.5 17.1 16.5 19.2
13.2 12.9 12.7 17.4 16.6 19.3 19.5 18.5 18.4 18.9
12.5 15.3 15.8 14.3 14.1 17.9 17.5 17.3 16.9 18.7
Solution
Plant Dry weight in mg Number of plants
10.00 – 11.99 2
12.00 – 13.99 6
, 14.00 – 15.99 7
16.00 – 17.99 8
18.00 – 19.99 7
Total
Definition of some Terms used in Frequency Distribution
Class interval: it is a symbol defining a class e. g. 4.4 – 4.9, 4.9 – 5.4, e.t.c.
Class limits: represents the end points of a class interval. The smaller number is the lower
class limit, while the larger number is the upper class limit
Class boundaries: The point of demarcation between a class interval and the next class
interval is called the class boundaries
Class size or width: It is the differences between the lower and the upper class boundaries
Grouped Frequency Distribution
The heights in inches of commonly grown herbs are shown below. Organize the data into a
frequency distribution with six classes, and make useful suggestions.
18 20 18 18 24 10 15 12 29 36
13 20 18 24 18 16 16 20 7
Solution:
Find the range of the data: Highest value – lowest value (36 – 7 =29)
The class width is given by = 4.8 (round it up to the nearest whole
number= 5)
Table 2.2: Frequency distribution for grouped data
Class limits Class Tally Frequency Cumulative Relative
boundaries frequency frequency (%)
5 – 10 4.5 -10.5 // 2 2 10.5
11 -16 10.5 – 16.5 ///// 5 7 26.3
17 -22 16.5 – 22.5 /////,/// 8 15 42.1
23 – 28 22.5 – 28.5 // 2 17 10.5
29 -34 28.5 – 34.5 / 1 18 5.3
STA 111 – ELEMENTARY STATISTICS
Lecture Note by DANIEL Deborah O.
COURSE OUTLINE
Frequency Distribution- Class Interval, Class Limits, Class Boundaries, Data Presentation, Bar
Chart, Histogram, Cumulative Frequencies And O-Give;
Measure of Location or Central Tendency – Mean, Median, Mode, Quartiles and Percentiles for
Ungrouped and Grouped Data;
Measure of Dispersion – Range, Standard Deviation, Variance, Moment, Skewness and Kurtosis;
Probability Theory – Basic Laws of Probability, Addition of Probabilities, Conditional
Probability;
Probability Distribution – Binomial Distributions, Poisson Distribution and Normal Distribution.
,FREQUENCY DISTRIBUTIONS
Classification or grouping of data into a set of classes reflecting the pattern of occurrences is
referred to as frequency distribution. The following examples illustrate the construction of
frequency distribution
(1) 1 5 3 4 1 3 2 5
1 4 1 3 2 0 1 2
1 2 0 2 1 4 5 3
Solution
Let 𝑥 represent these data values, we can use a frequency distribution to represent this set of data
by listing the x values with their frequencies in the table below
𝑥 0 1 2 3 4 5
𝐹 2 6 6 4 3 3
(1) The genotype of a group of 25 babies treated for jaundice at a public health centre are
as follows; AA AA AS AS AA AS AA AA SS AA SS AS AA AA AS AS
SS AA AS AS, AA, AA, SS, AS, AS
Solution
Genotype Number of babies
AA 11
AS 10
SS 4
Total 25
(3) The dry weights in mg of 30 seedlings of a pawpaw variety at germination are as
follows;
10.6 11.6 13.0 12.1 14.6 15.9 14.5 17.1 16.5 19.2
13.2 12.9 12.7 17.4 16.6 19.3 19.5 18.5 18.4 18.9
12.5 15.3 15.8 14.3 14.1 17.9 17.5 17.3 16.9 18.7
Solution
Plant Dry weight in mg Number of plants
10.00 – 11.99 2
12.00 – 13.99 6
, 14.00 – 15.99 7
16.00 – 17.99 8
18.00 – 19.99 7
Total
Definition of some Terms used in Frequency Distribution
Class interval: it is a symbol defining a class e. g. 4.4 – 4.9, 4.9 – 5.4, e.t.c.
Class limits: represents the end points of a class interval. The smaller number is the lower
class limit, while the larger number is the upper class limit
Class boundaries: The point of demarcation between a class interval and the next class
interval is called the class boundaries
Class size or width: It is the differences between the lower and the upper class boundaries
Grouped Frequency Distribution
The heights in inches of commonly grown herbs are shown below. Organize the data into a
frequency distribution with six classes, and make useful suggestions.
18 20 18 18 24 10 15 12 29 36
13 20 18 24 18 16 16 20 7
Solution:
Find the range of the data: Highest value – lowest value (36 – 7 =29)
The class width is given by = 4.8 (round it up to the nearest whole
number= 5)
Table 2.2: Frequency distribution for grouped data
Class limits Class Tally Frequency Cumulative Relative
boundaries frequency frequency (%)
5 – 10 4.5 -10.5 // 2 2 10.5
11 -16 10.5 – 16.5 ///// 5 7 26.3
17 -22 16.5 – 22.5 /////,/// 8 15 42.1
23 – 28 22.5 – 28.5 // 2 17 10.5
29 -34 28.5 – 34.5 / 1 18 5.3
