Descriptive Statistics: Tabular, Graphical, &
Numerical Method
In this module, we will consider ways to describe and represent data. We will consider
frequency distributions, measures of central tendency, variances, standard deviations,
percentiles, and quartiles.
How to Summarize Qualitative Data Using Tables &
Graphs
We will begin this section by looking at a frequency distribution. A frequency
distribution is a tabular representation of the summary data that shows the numerical
count of items in each class in the data set.
Example 2.1
Look at the following data set in Table One:
Table 2.1 is a list of cars sold at the Ajax Used Car Emporium for the month of July 2014.
The sales data displayed in this manner is not particularly useful to Ajax. Display the data
in the form of a frequency distribution.
Solution
, In order to create a frequency distribution, we count the number of each model of car
sold, then display this information in a table. The frequency distribution for the data is
shown in Table 2.2. The frequency distribution shows the number sold of each model of
car. By looking at this data, Ajax can learn which brands of cars sold better than the
others.
The frequency distribution tells us that the bestselling brand is Ford followed closely by
Nissan. On the other hand, the brand least sold was Jeep.
NOTE: For any frequency distribution, the classes must not be allowed to overlap. An
overlap will result in double counting an item and will lead to erroneous results. For
some types of data, such as the car brands in example 2.1, there is usually not much
chance of creating classes that overlap. However, when working with certain types of
data, particularly numerical data, care must be taken to ensure that the classes do not
overlap.
Next, we will consider relative frequency. Relative frequency is a calculated value that
represents the proportion of the items in each class. The following formula calculates the
relative frequency:
where n is the total count of all the classes being compared.
The relative frequency can be converted to the relative percentage by multiplying the
relative frequency by 100.
Relative Percentage of a Category = Relative Frequency of a
Category *100
Example 2.2
Numerical Method
In this module, we will consider ways to describe and represent data. We will consider
frequency distributions, measures of central tendency, variances, standard deviations,
percentiles, and quartiles.
How to Summarize Qualitative Data Using Tables &
Graphs
We will begin this section by looking at a frequency distribution. A frequency
distribution is a tabular representation of the summary data that shows the numerical
count of items in each class in the data set.
Example 2.1
Look at the following data set in Table One:
Table 2.1 is a list of cars sold at the Ajax Used Car Emporium for the month of July 2014.
The sales data displayed in this manner is not particularly useful to Ajax. Display the data
in the form of a frequency distribution.
Solution
, In order to create a frequency distribution, we count the number of each model of car
sold, then display this information in a table. The frequency distribution for the data is
shown in Table 2.2. The frequency distribution shows the number sold of each model of
car. By looking at this data, Ajax can learn which brands of cars sold better than the
others.
The frequency distribution tells us that the bestselling brand is Ford followed closely by
Nissan. On the other hand, the brand least sold was Jeep.
NOTE: For any frequency distribution, the classes must not be allowed to overlap. An
overlap will result in double counting an item and will lead to erroneous results. For
some types of data, such as the car brands in example 2.1, there is usually not much
chance of creating classes that overlap. However, when working with certain types of
data, particularly numerical data, care must be taken to ensure that the classes do not
overlap.
Next, we will consider relative frequency. Relative frequency is a calculated value that
represents the proportion of the items in each class. The following formula calculates the
relative frequency:
where n is the total count of all the classes being compared.
The relative frequency can be converted to the relative percentage by multiplying the
relative frequency by 100.
Relative Percentage of a Category = Relative Frequency of a
Category *100
Example 2.2
