Sampling And Measures Of Central Tendency And Dispersion

Sampling and Measures of Central Tendency and Dispersion

Introduction: Overall Job Satisfaction (OJS) was the variable selected for this exercise because it lends itself to measures of central tendency and dispersion. The data are quantitative and continuous in nature.

Data Selected: The instructions for the exercise suggested a sample of approximately 30 individuals from one of eight variables. There were 288 measures of OJS. Every ninth individual was selected resulting in thirty-two (32) unique scores. The data was sorted by gender (17 males, 15 females) as shown in the following table:

GENDER AGE DEPT POSITION TENURE OVERALL INTRINSIC EXTRINSIC

1 2 3 2 1 1.6 2.67 4

1 3 3 1 3 1.8 5.33 5.5

1 2 3 1 1 3.4 5.33 2

1 3 3 2 1 4 5.5 6

1 1 3 2 1 4 5.33 6.5

1 2 3 2 3 4.4 3.33 6

1 2 3 2 1 4.4 5.67 6

1 2 3 1 1 4.6 6.17 3

1 2 3 1 1 4.8 4.33 6

1 3 3 1 1 5 6.17 7

1 2 3 1 3 5.4 5 6

1 3 3 1 1 5.4 5.67 6.5

1 3 2 1 1 6.2 4.83 4

1 3 3 1 1 6.2 5 6

1 3 3 2 2 7 5 6

1 2 3 1 1 7 7 7

1 2 3 2 1 7 6.83 6

2 2 2 1 1 2.2 1 1

2 3 3 1 3 2.4 4.33 6

2 2 3 2 2 2.6 6 2

2 2 3 2 3 3.2 3 6

2 1 2 2 2 3.6 6 7

2 1 1 2 2 3.8 5 6

2 2 3 2 3 4.4 5.5 7

2 2 2 1 2 4.6 5 4

2 2 3 1 2 4.6 4.17 6.5

2 2 3 1 1 4.8 5.5 6

2 2 2 2 1 4.8 6.33 5

2 2 2 1 1 5.4 5.67 4

2 2 2 2 3 5.6 6 5

2 2 2 1 1 5.8 4.17 5

2 1 1 1 1 6 6.67 6

Measures of Central Tendency:

4.56 mean

4.6 median

4.4, 4.6 mode note: software did not identify 4.8,5.4,7

Measures of Dispersion:

6 range

2.137 variance

1.462 standard deviation

1.129 mean deviation

Discussion: Microsoft Excel software was used for all calculations.

The arithmetic mean (average) was calculated to be 4.56. It is understood that this measure of central tendency is affected by extreme scores.

The median (middle value) for this even numbered sample of 32 is 4.6. This value suggests that the mean is being affected by scores indicating some degree of dissatisfaction.

The distribution of the data in this sample has many modes in that OJS scores of 4.4, 4.6, 4.8, 5.4 and 7 appeared three times each. The visual determination of the mode could not be confirmed using Microsoft Excel software because when