Descriptive

statistics

1- Definition:

It is branch of statistics which deals with

quantitative information. It’s also known summary statistics

–

Descriptive

statistics aim actually to summarize or explore data of sample

instead of using these data to make predictions or inferences about population

of data (larger group from which sample is selected).

–

Descriptive

statistics summarizes quantitative data either by numerical measures

such as mean, mode, variance or visually organized forms such as bar charts,

tables, graph, histogram, frequency distribution tables, stem and leaf plot

–

Descriptive

statistics are distinguished from inferential statistics on

following basis. With descriptive statistics there are simple descriptions

about what data is trying to show done by analysis and summarizing these

collection of information. However in inferential statistics data is actually

used in different way where inferences and predictions are done which is beyond

immediate sets of data presented alone.

–

Descriptive

statistics simply present quantities data including numerical

facts and measures in much manageable form to be used in research studies

2- Types of descriptive statistics (Main types)

There

are two major types of descriptive statistics depending on whether simple

summaries provided by descriptive statistics are whether quantitative (these

include various descriptive measures such as mean variance) or visual (these

include simple-understand graphs and tables)

Ø Types of descriptive statistics:

1- Organize Data:

–

Tables

–

Graphs

2- Summarize Data:

–

Central Tendency.

–

Variation.

Summarizing

Data:

–

Central Tendency

(or Groups’ “Middle Values”)

ü Mean

ü Median

ü Mode

–

Variation (or

Summary of Differences Within Groups)

ü Range

ü Interquartile

Range

ü Variance

ü Standard

Deviation

Central

tendency

It actually indicates a

typical value which will be considered as one central number best summarizes

entire set of values or measurements (This calculates

a central value of a data set)

Central tendency measures

`1. Mean:

–

Mean=Sum of

values/number of values

–

It is known as

the ((average)).This actually calculated by adding all values in series of

observation divided by their total number

–

It’s the most

common measure of central tendency

–

Mean works best

if distribution of data is very even across range or distributes in

normal-curve shape

2. Median:

–

It’s considered

as middle value which divides set of observations into two equal halves

–

Median formula:

(N+1)/2

–

It’s considered

as better measure of central tendency than mean if your

data are skewed

–

It’s not

influenced by outliers like mean so best works in case of unbalanced

observations.

3. Mode:

–

It’s the value

which occurs with greatest value of frequency in a set of data

–

It’s useful when

differences are rare or when the differences are non-numerical

–

It’s not always

a central value and a set of data can have actually more than one mode

Measures

of Variation

Variation

or Dispersion refers to another value which actually indicates how far the measurements

are from the mean or from that central value:

Ø Range:

–

It’s the

difference between greatest and lowest value in a set of data

–

Range=X (max)-X

(min)

Ø Variance:

–

It is the mean

deviation of all values from the mean.

–

It’s calculated

by getting deviation of each value alone then suaring it to finally add all

squared deviations divided by their (total number minus one)

–

It considers all

values in series of observation but being in squared units make it unable to be

added or subtracted to mean

Ø Standard deviation:

–

It is actually

square root of variance

–

Standard

deviation is considered as the “average” degree to which scores

deviate from the mean.

3. Types of variables

In statistics, a

variable has two characteristics:

§ A

variable is an attribute that describes a person, place, thing, or idea.

Variables

can be qualitative (categorical) or quantitative (numeric).

Ø Qualitative. Qualitative

categories that result in descriptive values or labels. For example the breed

of a dog (e.g., collie, shepherd) the color of a ball (e.g., red, green) would

be examples of qualitative or categorical variables.

Ø Quantitative. Quantitative variables

are numeric. They represent a measurable quantity and can be presented

numerically. For example, what is the difference between having seven apples

and saying that they are delicious, we can count or measure the seven apples

but we can’t put a number for how delicious they are, saying you have seven

apples because they can be presented numerically is quantitative but saying

they are delicious is not quantitative that’s because you can’t measure or

write them in numbers.

4-importance

of descriptive statics

The importance of

descriptive statics

–

It enables us to

present data in a meaningful way.

–

Allows for a simpler interpretation of the data.

Therefore using descriptive statistics is useful in summarizing a group of data.