Descriptive statistics: the type of statistics used to summarize or

describe data. It deals with the presentation of numerical facts, or data in the

tables or graphs form, and with the methodology of analyzing the data.

There are two main types of descriptive statistics:

1- central tendency: central tendency is a score that indicates where the

center of distribution tends to be located. It tells us about the shape and

nature of the distribution.

Measures of central tendency:-

-The Mode

-The Median

-The Mean

The mode: the most frequently occurring score or the most frequent measurement.

Examples:

1-4-77-23-83-4-88-47-82-4

the mode is :4

64-3-99-21-36-7-9-12-7-11

the mode is :7

2-122-167-188-322-122-8-34

the mode is :122

*If no number is repeated in the data set, there is

no mode

Example:

5-3-66-25-12-75-28-27-92

no mode

– Median

the median: If there is a number values in data set, then the median is the

mean of the two middle values.

*the median is a best measure of central

tendency.

for the data set : 6-9-1-2-6-5-1

arrange from lowest to highestd : 1-1-2-6-6-9

the median is the mean of 2 and 6

(2+6)÷2

=4

Examples:

132-139-131-138-132-139-133-137-139

1

Rearrange from lowest to highest

131-132-132-133-137-138-139-139-139

Middle value – 137

The median is : -137

25-10-16-25-12-22-20-23-13-10

Rearrange from lowest to highest:

10-10-12-13-16-20-22-23-25-25

Middle values – 16 and 20

Median = (16 + 20)/2 = 18

The Median is = 18

Mean: The summation of all data

values/number of data values

Examples:

Calculate the mean:

Length(m)

5.3

2.8

3.6

3.9

2.7

4.8

4.2

6.2

5.9

5.1

4.6

5.3

6.9

=(5.3+2.8+3.6+3.9+2.7+4.8+4.2+6.2+5.9+5.1+4.6+5.3+6.9)/3

=613

=4.7m

2-types of variability:

2

-range

-standard deviation

-variance

Range: the range is simply the difference between the highest and lowest number

in a set of numbers.

to measure the range we need :

-minimum value

-maximum value

variance: variance is the average of the squares of the deviations of the

observed numbers from mean .

– the square will always give positive values

standard deviation: the standard deviation (std dev) is the average deviation

of the values from the mean or the average spread.

– it is always positive

-the std dev is a basic building block for analyzing our data.

Types of variables:

– qualitative

– quantitative

Quantitative data: consist of values representing counts or measurements .

Qualitative data (or non- numeric ): consist of values that can be placed into

non numeric categories .

two levels of qualitative data:

Nominal level (by name)

– no natural ranking or ordering of the data exists.

Ordinal level ( by order )

-provides an order , but can not get a

precise mathematical difference between levels.

Importance of descriptive statistics :

the descriptive statistics is very important because we can use it to make or

measures graphs and charts and its very important to measure central tendency

and useful to summarize the data or values.