Basic statistics

Basic statistics

Statistics:

Like many other sciences Statistics is a developing discipline. It is not static. It has gradually developed during last few decades. In different times, it has been defined in different manners

A.L. Bowley defined statistics as

‘Statistics may be called the science of counting’.

A definition due to W.I. King is

‘Statistics may be defined as the science of collecting, organizing, presenting, analyzing and interpreting numerical data and making valid inferences on the base of the data.’

Types of statistics:

There are two types of statistics

1. Descriptive statistics

2. Inferential statistics.

1. Descriptive Statistics: Descriptive statistics involve graphical and numerical procedures that are used to summarize and process data and to transform data into information.

Example:

A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answer.

2. Inferential Statistics: inferential statistics are used to make inferences about a population from a sample in order to generalize (make assumptions about this wider population) and/or make predictions about the future. Inferential statistics provide the bases for prediction, forecasts and estimates that are used to transform information into knowledge.

Example:

TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewer

Frequency Distribution

Frequency Distribution

A Frequency Distribution is a grouping of data into mutually exclusive categories showing the number of observations in each class.

Class limit: The class limits are the lowest and the highest values that can be included in the class.

Class interval:  The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class. The class intervals should be equal. It is denoted here by i

Class Frequency: The number of observations in each class. It is denoted here by f. 

Class Midpoint: A point that divides a class into two equal parts.  This is the average of the upper and lower class limits.

Construction of frequency distribution:

           

Example:

Mr. Rahman is a professor of X University.  He wishes prepare to a report showing the number of hours per week students spend studying.  He selects a random sample of 30 students and determines the number of hours each student studied last week.  

  

15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6.

Organize the data into a frequency distribution

Step One:  First arrange the data in ascending order.  Then we get the data as:

10.3, 12.9, 12.9, 13.5, 13.7, 14, 14.2, 15, 15.4, 15.7, 16.6,17.1, 17.4, 17.8, 18.3, 18.3, 18.6,  18.9, 19.7, 20.3, 20.7, 20.8, 21.4, 23, 23.2, 23.7, 26.1, 27.1, 29.8, 33.8,.

Step Two: Decide on the number of classes using the formula

                                   

                        Where k=number of classes

                        n=number of observations

o        There are 30 observations so n=30.

o        Two raised to the fifth power is 32.

o        Therefore, we should have at least 5 classes, i.e., k=5.

Step Three: determine the class interval or width using the formula

Round up for an interval of 5 hours.

Set the lower limit of the first class at 7.5 hours, giving a total of 6 classes.

Step Four:  Set the individual class limits and

Steps Five and Six:  Tally and count the number of items in each class.

Hours studying	Tally	Frequency, f
7.5 up to 12.5	I	1
12.5 up to 17.5	IIII IIII II	12
17.5 up to 22.5	IIII IIII	10
22.5 up to 27.5	IIII	5
27.5 up to 32.5	I	1
32.5 up to 37.5	I	1