Statistics Homework: Data Organization and Presentation, Lesson Two

This assignment solution covers the essential concepts of data organization and presentation in statistics. It begins with an introduction to the importance of organizing raw data into a meaningful format for statistical analysis, including classification and tabulation. The solution then delves into frequency distribution, explaining the steps involved in its construction and what it reveals about the data. The document discusses different types of data classification (chronological, geographical, qualitative, and quantitative) and methods of data presentation using graphs, curves, and charts, such as bar charts, histograms, ogives, pie charts, Pareto charts, time series graphs, and stem-and-leaf plots. The assignment includes detailed solutions to review questions, which involve constructing frequency distributions, histograms, frequency polygons, and various types of frequency distributions. The document also provides guidance on selecting appropriate diagrams for different data types and presents examples of how to visualize data effectively. This resource is contributed by a student to be published on the website Desklib. Desklib is a platform which provides all the necessary AI based study tools for students.

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Lesson Two
Data Organization and Presentation
Learning Outcomes
After completing this lesson you should be able to
 arrange raw data in an array and then classified data to construct a frequency tab
cumulative frequency table
 transform frequency tables into a relative frequency and percentage distributions
 make the most suitable choice of method of presentations for a given set of data
2.1 Introduction
So far you know how to collect data. So what do we do with the collected data next?
Now you have to present the data you have collected so that they can be of use. Thus the
collected data also known as raw data are always in an unorganized form and need to
be organized and presented in a meaningful and readily comprehensible form in order
to facilitate further statistical analysis. We can present the collected data in follow
ways:
 Classification and Tabulation
 Diagrammatic Presentation
 Graphical Presentation
2.2 What is Classification of Data?
Classificationis the process of arranging things in the groups according to their
resemblances,similarity, or identity. For example,students in your class may be
grouped according to their sex, age, marital status etc.
The following are the main objectives of classifying the data:
 It condenses the mass of data in an easily assailable form.
 It eliminates unnecessary details.
 It facilitates comparison and highlights the significant aspect of data.
 It enables one to get a mental picture of the information and helps in drawing
inferences.
 It helps in the statistical treatment of the information collected
2.2.1 Types of Classification
Broadly, we can classify the data in following four different forms:
 Chronological or Temporal classification- the collecteddata are arranged
according to the order of time expressed in years, months, weeks etc. The data
are generally classified in ascending order of time
 Geographical or Spatial Classification- the data are classified according to
geographicalregion or place. For indicating immediatecomparison,the
observations are either classified in the alphabetical order of the reference places
or in the order of size of the observation

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 Qualitative classification - data are classified on the basis of some attributes or
quality like sex, literacy, religion, employment, etc. Such attributes cannot b
measured along with a scale.
 Quantitative classification - the collected data are grouped with reference to the
characteristics,which can be measuredand numerically describedsuch as
height, weight, sales, imports, age, income, etc. Frequency distribution is widely
used method in this classification.
2.3 Frequency Distribution
The easiest method of organizing data is a frequency distribution, which converts raw
data into a meaningful pattern for statistical analysis.
The following are the steps of constructing a frequency distribution:
 Specify the number of class intervals. A class is a group (category) of interest. No
totally accepted rule tells us how many intervals are to be used. Between 5 and
20 class intervals are generally recommended. Note that the classes must be both
mutually exclusive and all-inclusive. Mutually exclusive means that classes must b
selected such that an item can't fall into two classes, and all-inclusive classes are
classes that together contain all the data.
 When all intervals are to be the same width, the following rule may be used to
find the required class interval width:
W = (L - S) / K
where: W= class width, L= the largest data, S= the smallest data, K= No. of classes
What Frequency Distribution Tells Us:
1. It shows how the observations cluster around a central value; and
2. It shows the degree of difference between observations.
Stated & True Class Limits:
True Classes are those classes such that the upper true (or real) limit of a class is the sam
as the lower true limit of the next class.
Cumulative Frequency Distribution:
When the observations are numerical, cumulative frequency is used. It shows the total
number of observations which lie above or below certain key values.
Cumulative Frequency for a population = frequency of each class interval + frequencies
of preceding intervals. For example, the cumulative frequency for the above problem is:
3, 5, 9, and 10.
2.4 Presenting Data:
Graphs, curves, and charts are used to present data. Bar charts are used to graph the
qualitative data. The bars do not touch, indicating that the attributes are qualitative
categories, variables are discrete and not continuous.
Histograms are used to graph absolute, relative, and cumulative frequencies.
Ogive is also used to graph cumulative frequency. An ogive is constructed by placing a
point corresponding to the upper end of each class at a height equal to the cumulative

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frequency of the class. These points then are connected. An ogive also shows the relative
cumulative frequency distribution on the right side axis.
 A less-than ogive shows how many items in the distribution have a value less than
the upper limit of each class.
 A more-than ogive shows how many items in the distribution have a value greater
than or equal to the lower limit of each class.
Pie chart is often used in newspapers and magazines to depict budgets and oth
economicinformation.A completecircle (the pie) representsthe total number of
measurements. The size of a slice is proportional to the relative frequency of a particular
category. For example, since a complete circle is equal to 360 degrees, if the rel
frequency for a category is 0.40, the slice assigned to that category is 40% of 3
(0.40)(360)= 144 degrees.
Pareto chart is a special case of bar chart and often used in quality control. The purpose
of this chart is to show the key causes of unacceptable quality. Each bar in the chart
shows the degree of quality problem for each variable measured…………………………
Time series graph is a graph in which the X axis shows time periods and the Y axis
shows the values related to these time periods…………………………………..
Stem-and-leaf plots offer another method for organizing raw data into groups. These
types of plots are similar to the histogram except that the actual data are displayed
instead of bars. The stem-and-leaf is developed by first determining the stem and then
adding the leaves. The stem contains the higher-valued digits and the leaf contains the
lower-valued digits. For example, the number 78 can be represented by a stem of 7 and a
leaf of 8. Thus, the numbers 34, 32, 36, 20, 20, 22, 54, 55, 52, 68, and 63 can be grouped
follows:
Stem...............Leaf
2....................0..0..2
3....................2..4..6
4
5....................2..4..5
6....................3..8
Steps to Construct a Stem and Leaf Plot:
 Define the stem and leaf that you will use. Choose the units for the stem so that
the number of stems in the display is between 5 and 20.
 Write the stems in a column arranged with the smallest stem at the top and the
largest stem at the bottom. Include all stems in the range of the data, even if there
are some stems with no corresponding leaves.
 If the leaves consist of more than one digit, drop the digits after the first. You
may round the numbers to be more precise, but this is not necessary for the
graphical description to be useful.
 Record the leaf for each measurement in the row corresponding to its stem. Omit the
decimals, and include a key that defines the units of the leaf.

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Review Questions
1. Table 2 shows a frequency distribution of the lifetimes of 400 electric bulbs.
Table 2: Life times of radio tubes tested
Lifetime (hrs) Number of Tubes
500-549 12
550-599 48
600-649 58
650-699 72
700-749 68
750-799 62
800-849 42
850-899 28
900-949 10
Total 400
With reference to the table 2 determine the
i. Upper limit of the fifth class
ii. Lower limit of the eighth class
iii. Class mark of the seventh class
iv. Class boundaries of the last class
v. Class interval size
vi. Frequency of the fourth class
vii. Relative frequency of the sixth class
viii. Percentage of tubes whose lifetimes do not exceed 600hrs
ix. Percentage of tubes with lifetimes greater than or equal to 900hrs
x. Percentage of tubes whose lifetimes are at least 500 but less than 1000 hrs
2. Table 3: Lengths of iron bars in Cm
135 164 150 133 142 126 149 157
146 158 140 147 136 148 152 144
166 126 138 176 163 118 154 165
146 172 142 145 134 153 140 134
160 145 135 142 150 156 145 128
Using the data in table 3 Construct;
i. A frequency distribution
ii. A histogram
iii. A frequency polygon for the length distribution
3. Using the data in table 1 construct;
i. A relative or percentage frequency distribution
ii. A cumulative frequency distribution
iii. A percentage cumulative frequency distribution
iv. A histogram
v. A relative frequency histogram
vi. A frequency polygon
vii. An ogive
viii. A percentage ogive
ix. An “or more” cumulative frequency distribution
x. An “or more” ogive

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5. Name the different types of diagrams commonly used and mention the situations
where the use of each type of diagram would be appropriate
6. The following data relate to monthly income and expenditure under different heads
for families. Show these data by a suitable diagram.
Item of
Expenditure
Family A (monthly
income Rs 15,000)
Family B (monthly
income Rs 18,000)
Food 4,000 4,800
Clothing 3,500 4,000
Rent 3,000 4,000
Education 2,500 3,500
Fuel and lighting 1400 800
Others 600 900
7. The data given below pertain to R&D expenditure by public, private and industrial
sectors for three years. You are required to draw a suitable diagram to show these
data. (You may avoid the fractions by rounding them off.)
Sector R&D Expenditure (Rs)
2002 2003 2004
Public 614.61 827.58 736.05
Private 1,218.87 1,527.07 1,896.96
Industry 1633.33 2,154.65 2,233.01