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):

AA B A A E AA AA

P E AA B E AA E

E B E A B P

a- Construct frequency distribution

b- Calculate the relative frequencies and percent age of all categories

c- What percentage of these students ranked this instructor as excellent or above average?

d- Draw a bar graph for the relative frequency distribution.

e- 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

E 6

AA 5

A 3

B 4

P 2

N = 20

Relative frequency = Class frequency/ total frequency

Percentage frequency = Relative frequency * 100

b-

Category Frequency relative freq. % freq. Angle size

E 6 6/20 = 0.3 30% 108

AA 5 5/20 = 0.25 25% 90

A 3 3/20 = 0.15 15% 54

B 4 4/20 = 0.2 20% 72

P 2 2/20 = 0.1 10% 36

N = 20 1 100% 360

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.

c- The columns are positioned over a label that represents a categorical variable.

d- 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:

24 32 27 23 33 33 29 25 23 28

21 26 31 22 27 33 27 23 28 29

31 35 34 22 26 28 23 35 31 27

a- Construct a frequency distribution using classes

21-23, 24-26, 27-29, 30-32, and 33-35

b- Calculate the relative frequencies and percentages for all classes.

c- Construct a histogram and a polygon for the percentage distribution.

d- 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 7