# Statistics: Preliminaries

## What is Statistics

Statistics has three meanings:

1. Data (table or a series of values)
Light speed experiment
Expt Run Speed
001 1 1 850
002 1 2 740
003 1 3 900
004 1 4 1070
005 1 5 930
006 1 6 850
1. Plural of statistic (formula)
2. Method of analyzing and predicting data

## Data

Data: Information expressed in numbers (usually)

10, 23, 6, 16, 19, 25, 14, 12, 22, 28, 4, 21, 2, 7, 17

## Types of Data

1. Primary Data: Collected directly
2. Secondary Data: Fetched from someone else
Examples

## Unorganized and Organized Data

40, 39, 31, 38, 40, 40, 34, 39, 31, 38, 37, 30, 31, 37, 35, 37, 36, 35, 39, 39

x Freq
30 1
31 3
34 1
35 2
36 1
37 3
38 2
39 4
40 3

## Frequency Distribution

X = 11, 15, 16, 18, 20, 22, 25

Class Tally Frequency
11-15 || 2
16-20 ||| 3
21-25 || 2

## Construction

Range = (Highest value - Lowest value) + 1

X = 11, 15, 16, 18, 20, 22, 25

Range of X = ?

Class Interval

$$(11-15) \rightarrow (15-11+1)= 5$$, not 4

• $$(20-24) \rightarrow ?$$
• Number of class = $$\frac{Range}{Interval}$$
• Interval = ?

## Example of Frequency Distribution

X = 32, 20, 34, 17, 15, 40, 5, 18, 44, 28, 49, 27, 8, 29, 45, 39, 3, 35, 46, 37, 50, 36, 2, 4, 7, 24, 42, 31, 19, 14

Distribution

Range = ?

Let, class interval = 5

Number of class = ?

• Now, construct

## Interpretation

Class Frequency
11-15 2
16-20 5
21-25 9
26-30 10
31-35 3
• What have you known from this frequency distribution?
• What is the benefit of organizing?

# Diagrams

## Histogram

• Make sure class intervals are continuous

Continuous or exclusive: (10-15); (15-20); (20-25) Discontinuous/Inclusive: (10-14); (15-19)

• If discontinuous $$\rightarrow$$ convert
• Add 0.5 to upper limit and subtract 0.5 from lower limit
$$\downarrow$$

## Histogram Example

Interval Frequency
20-30 5
30-40 12
40-50 30
50-60 40
60-70 20
70-80 13
80-90 3
90-100 2

Write its interpretation in 3-5 sentences.

## Make a Histogram

Class Interval Continuous CI Frequency
11-20 10
21-30 20
31-40 35
41-50 20
51-60 15
61-70 10
71-80 8
81-90 5
91-100 3

Histogram

## Construction of Pie Chart

Fruit Production (f) Angle
Mango 35
Litchi 20
Guava 40
Banana 25

Find angles and plot them on the circle

$$Angle = \frac{f_i}{\Sigma f_i}\times 360$$

## When to Use Pie Chart

• Pie: For data that are part of a whole
• For all categorical data
US Races
Race Percentage
White 61.6
Black 12.4
Multiracial 10.2
Asian 6.0
Others 9.8
Year Population
1901 87
1991 106
2001 124
2011 142

## Bar Chart vs Histogram

Quantitative Data $$\to$$ Histogram

## [1] 85 79 70  6 32  8 17 93

Qualitative Data $$\to$$ Bar Diagram / Pie Chart

BD Religions
Religion Percentage
Islam 90.4
Hinduism 8.5
Buddhism 0.6
Christianity 0.4
Others 0.1