Egypt_cairo
Egypt_cairo
Organizing Data
– Raw Data
– Organizing and graphing qualitative Data
– Relative frequency and percentage distributions.
Example
The following are responses of 20 students of a business statistics class who were asked to evaluate their instructor. The students were asked to choose one of five answers: Excellent (E), Above Average (AA), Average (A), Below Average (B) and Poor (P):
Construct frequency distribution
Calculate the relative frequencies and percent age of all categories
What percentage of these students ranked this instructor as excellent or above average?
Draw a bar graph for the relative frequency distribution.
Draw the Pie chart.
Solution
Frequency Distribution
A frequency distribution for quantitative data lists all the classes (Intervals) and the number of values that belong to each class. Data presented in the form of a frequency distribution are called grouped data.
a- The frequency distribution table is
Category
Frequency
N = 20
Relative frequency = Class frequency/ total frequency
Percentage frequency = Relative frequency * 100
Category
Frequency
relative freq.
% freq.
Angle size
6/20 = 0.3
5/20 = 0.25
3/20 = 0.15
4/20 = 0.2
2/20 = 0.1
N = 20
C- 30%+25% = 55%.
Bar charts and histograms are used to compare the sizes of different groups.
Bar Charts
A bar chart is made up of columns plotted on a graph. Here is how to read a bar chart.
The columns are positioned over a label that represents a categorical variable.
The height of the column indicates the size of the group defined by the column label.
e- The pie chart is a circle divided into portions that represent (frequency / relative frequency / Percentages) of a population or a sample belonging to different categories.
Angle size = Relative frequency X 360
Organizing and Graphing Quantitative Data
Example
The following are the daily production of computers for 30 days:
Construct a frequency distribution using classes
21-23, 24-26, 27-29, 30-32, and 33-35
Calculate the relative frequencies and percentages for all classes.
Construct a histogram and a polygon for the percentage distribution.
For what percentage of days is the number of computer terminals produced in the interval 27 to 29?
Solution
a- The frequency distribution table is
interval
Freq.
21 – 23