Statistics: Preliminaries

Abdullah Al Mahmud

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

Histogram Example 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

Pie Chart

Construction of Pie Chart

Fruit production in Bangladesh (made-up data)

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
Bangladesh Population
Year Population
1901 87
1991 106
2001 124
2011 142

Pie vs Bar Chart

Pie Chart

Click to see large image

Bar Chart

Click to see large image

Donut Chart

To see how they are made, click here

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

Short-cut Method for AM