This document discusses statistical procedures and their applications. It defines key statistical terminology like population, sample, parameter, and variable. It describes the two main types of statistics - descriptive and inferential statistics. Descriptive statistics summarize and describe data through measures of central tendency (mean, median, mode), dispersion, frequency, and position. The mean is the average value, the median is the middle value, and the mode is the most frequent value in a data set. Descriptive statistics help understand the characteristics of a sample or small population.

1. STATISTICAL PROCEDURES
AND THEIR APPLICATIONS
Presented By:
Muhammad Nafees
@nafeesupdates

2. WHAT IS STATISTICS ?
Statistics is a discipline that concerns with the
collection,organization,analysis,interpretation,and presentation of
data.
• Statistic is the score of each individual or a singular data(concerned with
indivisual data).
• Statistics is the process of designing, comparing, interpreting and
analysing data(concerned with the sample or group of data).

3. Basic terminology of Statistics :
• Population –It is actually a total collection of set of individuals or
objects or events whose properties are to be analyzed e.g all patients
treated at a particular hospital last year or total batch of tablets formed in
industry last month.
• Sample –It is the subset or representative part of a population e.g the
patients selected to fill out a patient-satisfaction questionnaire or no of
tablets selectected for quality tests.

4. CONTINUE……..
• Parameter- A numerical measure that describes a characteristic of a
population e.g average , mean , standard deviation
the average of all patients who are very satisfied with the care they received.
• Variable- Any characteristic,number,or quantity of an item or an
individual that can be measured or count e.g age , income , eye colour
the household income of patients visit hospital last year.

5. CONTINUE……
• Variables may be of following types
1.Categorical Variables (e.g Gender, a variable that has the categories
male and female).
2.Numerical Variables
a)Discrete values (countable e.g number of students in a class)
b)Continuous values (measureable e.g height or weight of students)

6. TYPES OF STATISTICS:
Statistics have majorly categorised into two types:
1.Descriptive statistics (describe or summarize data)
2.Inferential statistics (make prediction or generalization from that data)

7. CONTINUE…..
Descriptive statistics are also categorised into four different categories:
a) Measure of central tendency
Measure of Central Tendencies are the mean, median and mode of the data
b) Measure of dispersion/Variability
Range, Variance, Dispersion, Standard Deviation are Measures of
Dispersion/Variability. It identifies the spread of data.

8. CONTINUE…..
c) Measure of frequency
Measure of Frequency displays the number of times a particular
data occurs e.g average , percentage
d) Measure of position
Measure of Position describes the percentile and quartile ranks.

9. CONTINUE……

10. Descriptive Statistics
Descriptive statistics simply describes and summarizes the data usually in
the form of graphs or charts.
Descriptive statistics uses data that provides a description of the population
either through numerical calculation or graph or table.It provides a graphical
summary of data. It is simply used for summarizing objects, etc
 It describes a sample/small population rather than a large population
 The process involves taking a potentially large number of data points in the
sample and reducing them down to a few meaningful summary values and
graphs. This procedure allows us to gain more insights and visualize the data
than simply pouring through row upon row of raw numbers!

11. CONTINUE…..
Descriptive statistics represent the available data sample and does not
include theories, inferences, probabilities, or conclusions. That’s a job
for inferential statistics.
With descriptive e statistics, there is no uncertainty because you are
describing only thpeople or items that you actually measure(sample).
You’re not trying to infer properties about a larger population

12. CONTINUE…..
Suppose we want to describe the test scores in a specific class of 30 students. We
record all of the test scores and calculate the summary statistics and produce
graphs.
Sr# Marks Sr# Marks Sr# Marks Sr# Marks Sr# Marks
1 65 6 80 11 75 16 85 21 80
2 80 7 65 12 80 17 75 22 70
3 75 8 85 13 70 18 90 23 85
4 85 9 75 14 95 19 75 24 80
5 70 10 80 15 75 20 85 25 95
Sr# Marks
26 75
27 80
28 75
29 85
30 75

13. Graphical Representation

14. Types of Descriptive Statistics
There are four types of descriptive statistics
1. Measures of Frequency:
Measure of Frequency displays the number of times a particular data occurs e.g average ,
percentage , frequency.
• Count, Average, Percentage.
• Shows how often something occurs.
• Use this when you want to show how often a response is given.

15. Frequency Table
DATA VALUE FREQUENCY
RELATIVE
FREQUENCY
CUMULATIVE RELATIVE
FREQUENCY
2 3 3/20 or 0.15 0.15
3 5 5/20 or 0.25 0.15 + 0.25 = 0.40
4 3 3/20 or 0.15 0.40 + 0.15 = 0.55
5 6 6/20 or 0.30 0.55 + 0.30 = 0.85
6 2 2/20 or 0.10 0.85 + 0.10 = 0.95
7 1 1/20 or 0.05 0.95 + 0.05 = 1.00

16. Percentage and Average
Average
= (79% + 81% + 74% + 70% +82% +
85%) / 6
Average=78.50%

17. Types of Descriptive Statistics
2.Measure of position:
A measure of position determines the position of a single value in relation to
other values in a sample data set.
Unlike the mean and the standard deviation, descriptive measures
based on quantiles are not sensitive to the influence of a few
extreme observations. For this reason, descriptive measures based
on quantiles are often preferred over those based on the mean and
standard deviation (Weiss 2010).

18. Continue…..
 Quantiles are cut points dividing the range of the data into
contiguous intervals with equal probabilities.
 Quartiles divide the data four (4) equal parts.
 Quintiles divide a data set into fifths (5) equal parts.
 Deciles divide a data set into ten (10) equal parts.
 Percentiles divide it into hundred (100) equal parts. Note that the
median is also the 50th percentile.

20. Types of Descriptive Statistics
3.Measure of Central Tendency
A measure of central tendency is a single value that attempts to
describe a set of data by identifying the central position within that set
of data.
 Measures of central tendency are sometimes called measures
of central location or classed as summary statistics. it suggests
that it is a value around which the data is centred
The mean, median and mode are all valid measures of central
tendency, but under different conditions, some measures of
central tendency become more appropriate to use than

21. Mean:
The mean is equal to the sum of all the values in the data set
divided by the number of values in the data set.
The mean (or average) It can be used with both discrete and continuous
data, although its use is most often with continuous data.
 So, if we have n values in a data set and they have values X1, X2, …,Xn, the
sample mean𝒙, usually denoted by "x bar“.
Formula:
Mean of Sample = X1 + X2 + X3 ,…….,Xn/n
𝒙 = ƩX/n
Mean of population = µ = ƩX/n

22. Characteristics of Mean:
The mean is essentially a model of your data set. You will notice,
however, that the mean is not often one of the actual values that you
have observed in your data set.
 However, one of its important properties is that it minimises error in
the prediction of any one value in your data set. That is, it is the value
that produces the lowest amount of error from all other values in the
data set.
An important property of the mean is that it includes every value in
your data set as part of the calculation.
The mean is the only measure of central tendency where the sum of
the deviations of each value from the mean is always zero.
Mean is susceptible to the influence of outlier and also not usefull
when data is skewed

23. Examples

25. Median:
The median is the middle score for a set of data that has been
arranged in order of magnitude.
Median, in statistics, is the middle value of the given list of data, when
arranged in an order.
 The arrangement of data or observations can be done either
in ascending order or descending .
The median is less affected by outliers and skewed data.

26. Median Formula:
Median formula is different for even and odd numbers of observations.
Therefore, it is necessary to recognise first if we have odd number of
values or even number of values in a given data set.
Odd Number of Observations:
If the total number of observation given is odd, then the formula to
calculate the median is:
Median = {(n+1)/2}th term
where n is the number of observations
Even Number of Observations:
If the total number of observation is even, then the median formula is:
Median = [(n/2)th term + {(n/2)+1}th]/2
where n is the number of observations

27. Mode:
Mode is defined as the most frequent value in our data set.
 It is a value that has a higher frequency in a given set of values and
appears the most number of times. On a histogram it represents the
highest bar in a bar chart or histogram.
.

28. …..
Normally, the mode is used for categorical data where we wish to
know which is the most common category, as illustrated below:

29. …..
• However, one of the problems with the mode is that it is not unique,
so it leaves us with problems when we have two or more values that
share the highest frequency, such as

30. …..
 it will not provide us with a very good measure of central tendency
when the most common mark is far away from the rest of the data in
the data set, as depicted in the diagram below:

31. …..
It is not useful for continuous data because we are more likely not to
have any one value that is more frequent than the other.
• e.g weight of students.
• Summary of when to use the mean, median and mode
• Use the following summary table to know what the best
measure of central tendency is with respect to the
different types of variable.
Type of Variable
Best measure of central
tendency
Nominal Mode
Ordinal Median
Interval/Ratio (not skewed) Mean
Interval/Ratio (skewed) Median