# Concept

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)
1. Method of analyzing and predicting data

## 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

Range = ?

Let, class interval = 5

Number of class = ?

• Now, construct

## Interpretation

Class (Marks out of 40) 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?

## Cumulative Frequency

Class (Marks out of 40) Frequency Cumulative Frequency
11-15 2 2
16-20 5 7
21-25 9 16
26-30 10 26
31-35 3 29
• Why Useful??
• How to interpret?

## Variable

• Discrete: Any of the pre-specified number
• Continuous/Indiscrete: Any number between any two other numbers.
• Temperature
• Result of a die throw
• Mark of a subject
• GPA of a student

# Diagram

## 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

## Frequency Polygon

• Locate top midpoints of each bar of histogram
• Join the points by straight lines.
• How to draw without drawing a histogram first?

## Frequency Curve

Somoothed version of frequency polygon

## Ogives

Cumulative Frequency (CF) for Ogive
intervals CF
0-5 1
5-10 2
10-15 4
15-20 6
20-25 7
25-30 10

# Central Tendency

## Arithmetic Mean (AM)

• From Frequency Distribution: Use mid-values and multiply with frequencies

$AM = \frac 1 n \sum_{i=n}^n f_ix_i$

## AM in Short-cut Method

• WHY?
• Is this method really SHORT?

## Shortcut Method for AM

Calculate the mean in a smart way

## [1] 1009 1037 1047 1024 1013 1043
Show

## Shortcut Method Formula

Consider the values: 1005, 1010, 1015

If 1000 is subtracted: 5, 10, 15

If again divided by 5: 1, 2, 3

Converted Mean = 2

Original Mean = $$2 \times 5 + 1000=1010$$

Show