What Is Descriptive Statistics Help

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Introduction to descriptive statistics help:

Definition of Statistics:

In simple terms, statistics is termed as a branch of mathematics which basically deals with collection of data and its subsequent analysis and interpretation both qualitatively and quantitatively. In most of the cases the data is numerical, but there are also cases when the data is non-numerical such as relationship between objects.

Without statistics, it would be difficult to maintain anything numerical in nature and extremely difficult to go through the daily routines of life. Imagine watching a baseball match or basket match without knowing the score of each team or imagine going to a super mart trying to find the latest manufactured milk product without having the manufactured date printed on the milk product carton.

The person who is well versed in statistics is called a statistician and is supposed to have a good knowledge and understanding of the ways to collect data, maintain data, interpret/analyse data and finally present the data.

Help on Overview of Descriptive Statistics

Types of statistics:

There ...
... are many kinds of statistics being used out of which the most commonly used one is descriptive statistics which can be further sub-classified as numerical descriptive statistics and pictorial descriptive statistics.

Other forms of statistics are inferential statistics, psychological statistics, business statistics and so on.

Examples of Statistics

Numerical

1. Frequency distribution to find the frequency of different sets of data provided.

2. Central tendency to find the mean, media and mode

3. Dispersion to find the range, variance and standard deviation

Graphical

1. Histograms

2. Scatter Plot

3. Box Plot

Help with Detailed explanation on Descriptive statistics

Lets consider a sample data set containing the marks of 12 students in a math class test with the following marks. The students have been given marks out of a maximum marks of 25 with the pass marks being 10 out of 25.

9 , 11, 15, 13, 17 , 5 , 23 , 19 , 21 , 7 , 25, 15

Lets use descriptive statistics to find out the frequency distribution, central tendency and dispersion for the above set of value.

Frequency distribution

Using frequency distribution, we can find the percentage of passed students, failed students and students with full marks

Percentage of passed students = ( no of students passed / total no od students ) * 100 = (9/12) * 100 = 75%

Percentage of failed students = ( no of failed students / total no of students ) * 100 = (3/12) * 100 = 25 %

Pecentage of students with full marks = ( no of students with full marks/ total no of students) * 100 = (1/12) * 100 = 8.25 %

Central Tendency

Using central tendency we can find the Mean, Median and Mode of the above set of data.

Mean is the average marks of all the students combined which would sum of marks obtained by all the students divided by the total number of students

Mean = ( 5+7+9+11+13+15+15+17+19+21+23+25+) / 11 = 180 / 12 = 15

Hence 15 is the average marks of all the maths students put together

Median is the mark that is found at exactly the middle of the above set of marks when they are arranged in an ascending order.

For this purpose lets arrange the marks in an ascending order and find out the middle value.

5,7,9,11,13,15,15,17,19,21,23,25

In the above arrangement we could see that there are 2 value in the middle which is 15. Hence we add both these values and divide by 2 to arrive at the median which will give us an answer of 15

Finally lets find the mode of the above set of marks. Mode is nothing but the value which ocurrs most number of times

In the above set of marks we could see that 15 has ocurred twice and hence mode = 15

We could see from the above calculations that all the 3 values, Mean, Median and Mode are equal to 15 which would imply that the distribution of the marks among the math students is normal and uniform. It is also called as Bell Shaped distribution when the Mean, Median and Mode are same.

Dispersion

Dispersion helps us in finding the range variance and standard deviation.

Range is nothing but the difference between the highest and the lowest value. In the current set of data, 5 is the least value and 25 is the highest value which would mean 25 -5 = 20 is the range of the above distribution.

Variance is nothing but the sum of squares of mean marks minus individual marks divided by the total number of value minus 1

In short Variance = (a1-x)2 + (a2-x)2 + (a3-x)2 + .........+ (an-x)2 / ( n-1 )

where a1, a2 , a3 , a4 , .......... an are the marks and n is the number of marks which in our case is 12

Lets apply the above formulae to calculate the variance

Variance = (5-15)2 + (7-15)2 + (9-15)2 + (11-15)2 + (13-15)2 + (15-15)2 + (15-15)2 + (17-15)2 + (19-15)2 + (21-15)2 + (23-15)2 + (25-15)2 / ( 12 -1)

Variance = ( 100 +64 + 36 + 16 +4 + 0 + 0 + 4 + 16 + 36 + 64 + 100 ) / (12-1)

Variance = ( 440 ) / ( 11)

Variance = 40

Now that we have found out variance, lets find out standard deviation. Standard Deviation is nothing but square root of variance

Standard deviation = SQRT ( Variance )

Standard deviation = SQRT ( 40 )

Standard deviation = 6.324

Comprehend more on about Examples of Bias and its Circumstances. Between, if you have problem on these topics Define Census Please share your views here by commenting.