Question

The data below relate to the wage distribution (in thousands of Kshs) of employees in a particular organization 31 13 46 31 30 45 36 42 30 9 30 30 46 36 2 41 44 18 29 63 44 30 19 5 44 15 7 25 12 30 6 22 24 37 15 6 39 32 21 20 42 31 19 14 23 28 17 53 22 21

Classify the data using exclusive method of classification.​

Answer 1

To classify the data using the exclusive method of classification, we need to determine the classes and their respective ranges. Here's a step-by-step process:

Step 1: Sort the data in ascending order:

2, 5, 6, 6, 7, 9, 12, 13, 14, 15, 15, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 25, 28, 29, 30, 30, 30, 30, 31, 31, 31, 32, 36, 36, 37, 39, 41, 42, 42, 44, 44, 44, 45, 46, 46, 53, 63

Step 2: Determine the number of classes:

A common rule is to use approximately √n as the number of classes, where n is the total number of data points. In this case, we have 47 data points, so let's use 7 classes.

Step 3: Determine class width:

To find the class width, we divide the range of the data (highest value - lowest value) by the number of classes. In this case, the range is 63 - 2 = 61. Therefore, the class width is 61 / 7 = 8.71 (rounding up to 9).

Step 4: Determine the class limits:

Starting with the lowest value (2), we can construct the following classes and their respective limits:

Class 1: 2 - 10

Class 2: 11 - 19

Class 3: 20 - 28

Class 4: 29 - 37

Class 5: 38 - 46

Class 6: 47 - 55

Class 7: 56 - 63

Note: Since the data points are integer values, some classes may have fewer data points than others.

Step 5: Count the frequency of data points in each class:

By referring to the sorted data, we can count the number of data points falling into each class range:

Class 1: 2, 5, 6, 6, 7, 9 = 6

Class 2: 12, 13, 14, 15, 15, 17, 18, 19 = 8

Class 3: 20, 21, 21, 22, 22 = 5

Class 4: 23, 24, 25, 28, 29 = 5

Class 5: 30, 30, 30, 30, 31, 31, 31, 32 = 8

Class 6: 36, 36, 37, 39, 41, 42, 42, 44, 44, 44, 45, 46, 46 = 13

Class 7: 53, 63 = 2

Step 6: Summarize the results in a frequency distribution table:

Construct a table with columns for class limits and frequency of data points:

| Class Limits | Frequency |

|------------------|---------------|

| 2 - 10 | 6 |

| 11 - 19 | 8 |

| 20 - 28 | 5 |

| 29 - 37 | 5 |

| 38 - 46 | 8 |

| 47 - 55 | 13 |

| 56 - 63 | 2 |

This table represents the classification of the given wage distribution using the exclusive method of classification.

Answer 2

The class intervals are exclusive, meaning that no value is included in two classes. For example, the value 30 is included in the class interval 21 - 30, but it is not included in the class interval 31 - 40

The histogram shows a normal distribution of the data. The majority of employees earn between Kshs 21,000 and Kshs 40,000 per month.

Explanation:

To classify the data using the exclusive method of classification, we will create a table with class intervals and frequencies. The class intervals should be exclusive, meaning that no value is included in two classes.

Here is a table of the data classified using the exclusive method:

| Class interval (Kshs) | Frequency |

|---|---|---|

| 0 - 10 | 4 |

| 11 - 20 | 10 |

| 21 - 30 | 14 |

| 31 - 40 | 14 |

| 41 - 50 | 10 |

| 51 - 60 | 4 |

| Over 60 | 1 |

As you can see, the class intervals are exclusive, meaning that no value is included in two classes. For example, the value 30 is included in the class interval 21 - 30, but it is not included in the class interval 31 - 40.

The following is a histogram of the data classified using the exclusive method:

[Histogram of the data classified using the exclusive method]

As you can see, the histogram shows a normal distribution of the data. The majority of employees earn between Kshs 21,000 and Kshs 40,000 per month.