| PCC | Mahmud | Statistics | statmania.info |

Statistics has three meanings:

- Data (table or a series of values)

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 |

- Plural of statistic (formula)
- Method of analyzing and predicting data

Data: Information expressed in numbers (usually)

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

- Primary Data: Collected directly
- Secondary Data: Fetched from someone else

Examples

- A researcher collects rainfall data everyday for predicting future rainfall.
- An investigator collects family and geographical information of criminals.
- WHO tracks information of Covid-19 patients.
- An independent researcher uses information collected by WHO.
- A teachers borrowes marks graded by another teacher.

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 |

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

Class | Tally | Frequency |
---|---|---|

11-15 | || | 2 |

16-20 | ||| | 3 |

21-25 | || | 2 |

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 = ?

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

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?

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

\(\downarrow\)

Conversion

Continuous CI | Discontinuous CI |
---|---|

10-14 | 9.5-14.5 |

15-19 | 14.5-19.5 |

20-24 | 19.5-24.5 |

25-29 | 24.5-29.5 |

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.

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

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

\(Angle = \frac{f_i}{\Sigma f_i}\times 360\)

- Pie: For data that are part of a whole
- For all categorical data

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 |

Pie Chart

Bar Chart

Quantitative Data \(\to\) Histogram

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

Qualitative Data \(\to\) Bar Diagram / Pie Chart

Religion | Percentage |
---|---|

Islam | 90.4 |

Hinduism | 8.5 |

Buddhism | 0.6 |

Christianity | 0.4 |

Others | 0.1 |