# Chapter 2

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### Chapter 2:

Chapter 2 Descriptive Statistics: Tabular and Graphical Methods

### Graphically Summarizing Qualitative Data:

Graphically Summarizing Qualitative Data With qualitative data, names identify the different categories This data can be summarized using a frequency distribution Frequency distribution : A table that summarizes the number of items in each of several non-overlapping classes.

### Frequency Distribution:

Frequency Distribution A frequency distribution is a list of data classes with the count of values that belong to each class “Classify and count” The frequency distribution is a table

### Constructing a Frequency Distribution:

Constructing a Frequency Distribution Steps in making a frequency distribution: Find the number of classes Find the class length Form non-overlapping classes of equal width Tally and count

### Example Marks obtained by a student in a test:

Example Marks obtained by a student in a test 22 29 16 15 18 17 12 13 17 16 15 19 17 10 21 15 14 17 18 12 20 14 16 15 16 20 22 14 25 19 23 15 19 18 23 22 16 16 19 13 18 24 24 26 13 18 17 15 24 15 17 14 18 17 21 16 21 25 19 20 27 16 17 16 21

### Number of Classes:

Number of Classes Group all of the n data into K number of classes K is the smallest whole number for which 2 K  n In Examples n = 65 For K = 6, 2 6 = 64, < n For K = 7, 2 7 = 128, > n So use K = 7 classes

### Example Marks obtained by a student in a test:

Example Marks obtained by a student in a test 22 29 16 15 18 17 12 13 17 16 15 19 17 10 21 15 14 17 18 12 20 14 16 15 16 20 22 14 25 19 23 15 19 18 23 22 16 16 19 13 18 24 24 26 13 18 17 15 24 15 17 14 18 17 21 16 21 25 19 20 27 16 17 16 21

### Class Length:

Class Length Find the length of each class as the largest measurement minus the smallest divided by the number of classes found earlier (K) For Example (29-10)/7 = 2.7143 Lets us round off it to 3

### Seven Non-Overlapping Classes:

Seven Non-Overlapping Classes Class 1 10 to 13 Class 2 13 To 16 Class 3 16 to 19 Class 4 19 to 22 Class 5 22 days and less than 25 days Class 6 25 days and less than 28 days Class 7 28 days and less than 31 days

### PowerPoint Presentation:

Individual Observations Marks Obtained by 35 students in a Class Test 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6

### PowerPoint Presentation:

Formation of A Discrete Frequency Distribution

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 3 4 5 6 7 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 | 3 4 5 6 7 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 | 3 4 5 | 6 7 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 | 3 | 4 5 | 6 7 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 | 3 | 4 5 || 6 7 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 | 3 | 4 5 ||| 6 7 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 | 3 | 4 5 ||| 6 7 | 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 | 3 | 4 | 5 ||| 6 7 | 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 | 3 | 4 | 5 |||| 6 7 | 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 | 3 | 4 || 5 |||| 6 7 | 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 || 3 | 4 || 5 |||| 6 7 | 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 1 | 2 ||| 3 | 4 || 5 |||| 6 7 | 8 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 | 4 || 5 |||| 6 7 | 8 | 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 | 4 || 5 |||| 6 | 7 | 8 | 9 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 | 4 || 5 |||| 6 | 7 | 8 | 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 | 4 ||| 5 |||| 6 | 7 | 8 | 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 || 4 ||| 5 |||| 6 | 7 | 8 | 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 || 4 ||| 5 |||| 6 | 7 | 8 || 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 || 4 ||| 5 |||| 6 | 7 || 8 || 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 || 4 ||| 5 |||| 6 | 7 ||| 8 || 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 1 | 2 ||| 3 ||| 4 ||| 5 |||| 6 | 7 ||| 8 || 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 | 1 | 2 ||| 3 ||| 4 ||| 5 |||| 6 | 7 ||| 8 || 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 | 1 | 2 ||| 3 ||| 4 ||| 5 |||| 6 | 7 |||| 8 || 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 | 1 | 2 ||| 3 |||| 4 ||| 5 |||| 6 | 7 |||| 8 || 9 | 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 | 1 | 2 ||| 3 |||| 4 ||| 5 |||| 6 | 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 | 1 | 2 |||| 3 |||| 4 ||| 5 |||| 6 | 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 | 1 | 2 |||| 3 |||| 4 |||| 5 |||| 6 | 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 0 3 12 3 6 0 | 1 | 2 |||| 3 |||| 4 |||| 5 |||| 6 || 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 | 1 | 2 |||| 3 |||| 4 |||| 5 |||| 6 || 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 9 0 | 1 | 2 |||| 3 |||| 4 |||| 5 |||| 6 || 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 || 1 | 2 |||| 3 |||| 4 |||| 5 |||| 6 || 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 || 1 | 2 |||| 3 |||| 4 |||| 5 |||| 6 || 7 |||| 8 || 9 || 10 11 12

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 || 1 | 2 |||| 3 |||| 4 |||| 5 |||| 6 || 7 |||| 8 || 9 || 10 11 12 |

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 || 1 | 2 |||| 3 ||||| 4 |||| 5 |||| 6 || 7 |||| 8 || 9 || 10 11 12 |

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 0 || 1 | 2 |||| 3 ||||| 4 |||| 5 |||| 6 ||| 7 |||| 8 || 9 || 10 11 12 |

### Marks obtained by 35 students:

Marks obtained by 35 students 1 2 5 3 5 5 7 4 5 4 2 2 8 6 9 4 3 8 7 7 3 0 7 3 9 2 4 6 4 5 0 3 12 3 6 marks tallies Frequency 0 || 2 1 | 1 2 |||| 4 3 ||||| 6 4 |||| 5 5 |||| 5 6 ||| 3 7 |||| 4 8 || 2 9 || 2 10 0 11 0 12 | 1 Total 35