Organization and presentation of data

Question 1

Forms of arranging data

Answer 1

Arrays
Frequency tables
Stem and leaf plot
Tabulations: Simple tables and cross tabulation

Question 2

Arrays

Answer 2

Simple arrays

Frequency arrays

Question 3

Simple arrays

Answer 3

It is an arrangement of data in an ascending or descending order

Question 4

Frequency arrays

Answer 4

It is a series formed on the basis of frequency with which each item is repeated in a series.

Question 5

Steps in constructing a frequency array

Answer 5

1. Prepare a table with three columns
2. Put the item in the first column in an ascending order such that one item is recorded only
   once
3. Prepare the tally sheet in the second column marking one bar for an item. Make blocks of
   five tally bars to avoid mistakes in counting. Every fifth bar is shown by crossing the first
   four bars like ////.
4. Count the tally bar and record the total number in the third column.

Main limitation: it does not give the idea of the characteristics of groups. For example, it does not tell us how many students have obtained marks between 45 -50. It’s not possible to
compare characteristics of different groups

Question 6

Frequency distribution tables

Answer 6

• Lists categories of items along with their corresponding frequencies.
• The frequency for a particular category or class is the number of original items that fall into that class.
• The classes or categories refer to the groupings of a frequency table.
• The range is the difference between the highest value and the lowest value.
  (R = highest value – lowest value).
• The class width or class interval is the difference between two consecutive lower class limits or
  class boundaries.
• The class limits are the smallest or the largest numbers that can be included in the class: Lower class limits represents the smallest data value that can be included in the class. Upper class limits represents the highest data value that can be included in the class.
• The class boundaries are used to separate the classes so that there are no gaps in the frequency distribution. They are obtained by increasing the upper class limits and decreasing the lower
  class limits by the same amount so that there are no gaps between consecutive under classes. The
  amount to be added or subtracted is 0.5 the difference between the upper limit of one class and the lower limit of the following class.
• The class limits should have the same decimal place value as the data,
  but the class boundaries should have one additional place value.
• Class marks/mid value/mid points is the average value of two limits of a point.

Question 7

Guidelines for constructing a frequency distribution table

Answer 7

• The classes must be mutually exclusive. That is, each score must belong to exactly one class.
• The classes must be exhaustive meaning there should be enough classes to accommodate
  all data. Include all classes, even if the frequency might be zero.
• All classes should have the same width, to avoid a distorted view of data. One exception
  occurs when a distribution has a class that is open – ended such as “65 years or older”.
• The number of classes should be between 5 and 20.

Question 8

Process of Constructing a Frequency Table

Answer 8

1. Determine the range. (R = Highest Value – Lowest Value).
2. Determine the tentative number of classes (k). The number of classes is the least value of k such that 2^k>N. This involves some trying for different values of k e.g. if N=45 we can try 2^2=32 , this is less than 45, 2^6=64 which satisfies the condition 2^k>N therefore k=6.
3. Find the class width by dividing the range by the number of classes.(Always roundoff).
4. Write the classes or categories starting with the lowest score. Stop when the class already includes the highest score.
5. Determine the frequency for each class by referring to the tally columns and present the results in a table.

Question 9

Limitation of frequency distribution table

Answer 9

, while the frequency of each class is easy to
see, the original data points have been lost.

Question 10

Stem-and-Leaf Plots

Answer 10

It shows us potential patterns in the responses that may not be apparent in the original listing of the data

Question 11

Steps of constructing a stem and leaf plot

Answer 11

1. Find the least number and the greatest number in the data set.
2. Draw a vertical line and write the digits in the tens places from 1 to 3 on the left of the
   line. The tens digit form the stems.
3. Write the units digit to the right of the line. The units digits form the leaves.
4. Rewrite the units digits in each row from the least to the greatest.
5. Include an explanation. To analyze a stem and leaf plot look for peaks, gaps and symmetry.

Question 12

Tabulation:
Simple (one way)
Cross tabulation

Answer 12

A table is a systematic arrangement of statistical data in columns and rows.
Rows are horizontal arrangements while columns are vertical arrangements.
The purpose of a table is to simplify the presentation and to facilitate comparison.

Question 13

Essential parts of a table

Answer 13

Table number
Title of the table
Caption (Headings of columns)
Stub (Headings of rows)
Body
Head note (unit of measurement of data)
Foot note

Question 14

Simple (One-Way) Tables

Answer 14

only one characteristic is shown.

Question 15

Cross Tabulation

Answer 15

More than one characteristic is included in a table. They are a good way to compare two
subgroups of information.
Cross tabs allow you to compare data from two questions to determine
if there is a relationship between them.
Cross tabs are used most frequently to look at answers to a question among various demographic
groups. The intersections of the various columns and rows, commonly called cells, are the
percentages of people who answered each of the responses.

Question 16

Data presentation

Answer 16

Pictograms

Graphs presentation

Question 17

Pictograms

Answer 17

Data is represented using a self-explanatory pictorial symbol. They are
attractive and easy to remember but are limited when dealing with large quantities.

Question 18

Graphs

Answer 18

1. Bar graphs
2. Histograms
3. Line graphs
4. Pie charts
5. Pictograms
6. Frequency polygons
7. Cumulative frequency curve (ogive)

Question 19

Bar graphs

Answer 19

Device used to represent data that are either nominally or ordinally scaled. The height of the bar
represents the number of items in that category. The bars can be vertical or horizontal. The width of the bars and the gap between one bar and another should be uniform throughout

Question 20

Simple bar graphs

Answer 20

Used to represent only one variable. Only the length of the bars varies and
they are very easy to read. The limitation is that they can only present one classification or
category of data.

Question 21

Subdivided bar graphs

Answer 21

The bars are divided into more than one component. They require an index or a key to distinguish the different components. They are useful in presenting a set of
distribution ratios diagrammatically

Question 22

Multiple bar graphs

Answer 22

used to represent two or more interrelated data sets. Different shades or patterns can be used to distinguish between the bars. They are useful when making a comparison
between two or more related variables

Question 23

Percentage bar graphs

Answer 23

Useful in statistical work which requires portrayal of relative changes in data. The length of the bars is kept equal to 100 and segments are cut in the bars to represent the
components (percentages) of an aggregate

Question 24

Deviation bars

Answer 24

Used to represent net quantities such as net profit, net loss etc. The bars can have both negative and positive values. The positive values are shown above the base line and the
negative values below it.

Question 25

Pie chart

Answer 25

Used to show proportions of different categories of classes. They are less effective
than bar graphs when the categories are many. Not advisable to use if there are more than five or
six categories.

Question 26

Histograms

Answer 26

Displays data by using continuous vertical bars. The area of the each bar is proportional to the
frequency represented. Used for interval and ratio scale data. The scale along the horizontal axis is continuous. The width of the bars is equal to the class interval.
If the class intervals are equal take the frequency is taken on the vertical axis. When the class
intervals are unequal we have to adjust the frequencies otherwise the histogram would give a misleading picture. The frequency density is taken along the vertical axis. 
Cannot be drawn for distributions having open ended classes.

Question 27

Frequency density

Answer 27

frequency/class interval

Question 28

Difference between bar graph and histogram

Answer 28

A bar graph is one dimensional

only the height matters while a histogram is two dimensional, both height and width of the bars matter.

Question 29

Frequency polygon

Answer 29

A graph that displays the data using lines that connect points plotted for the frequencies at
the midpoints of the classes. They can be used to compare two or more frequency distributions
on the same graph which cannot be done with histograms.
They cannot be drawn for distributions having open ended classes.

Question 30

Cumulative frequency curve (ogive)

Answer 30

Represent the cumulative frequencies for
the classes in a frequency distribution.
Ogives are used to portray the number or proportion of cases above or below a given value.
They are also used to obtain graphically values such as the median, quartiles, deciles etc.