A company is interested in determining the strength of association between the
communication time of their employees and the level of stress-related problems observed
on job. A study of 120 assembly line workers reveals the following data:
|
| Stress | |||
|
| High | Moderate | Low | Total |
| Under 20 min | 10 | 10 | 15 | 35 |
| 20- 50 min | 15 | 10 | 25 | 50 |
| Over 50 min | 15 | 10 | 10 | 35 |
| Total | 40 | 30 | 50 | 120 |
To determine the strength of the association between communication time and the level of stress-related problems, we can analyze the given data using descriptive statistics. We can calculate the following measures:
-
Frequency Distribution: The table shows the frequencies of stress levels for three categories of communication time: under 20 minutes, 20-50 minutes, and over 50 minutes.
Stress Level Under 20 min 20-50 min Over 50 min Total High 10 15 15 40 Moderate 10 10 10 30 Low 15 25 10 50 Total 35 50 35 120 -
Proportions: We can calculate the proportion of employees in each category of stress level for each communication time category:
-
Under 20 min:
- High stress: 1035=0.286\frac{10}{35} = 0.286
- Moderate stress: 1035=0.286\frac{10}{35} = 0.286
- Low stress: 1535=0.429\frac{15}{35} = 0.429
-
20-50 min:
- High stress: 1550=0.3\frac{15}{50} = 0.3
- Moderate stress: 1050=0.2\frac{10}{50} = 0.2
- Low stress: 2550=0.5\frac{25}{50} = 0.5
-
Over 50 min:
- High stress: 1535=0.429\frac{15}{35} = 0.429
- Moderate stress: 1035=0.286\frac{10}{35} = 0.286
- Low stress: 1035=0.286\frac{10}{35} = 0.286
-
-
Association Analysis: To quantify the
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Describe the various types of measures of skewness. If the first four raw moments are 10, 100, 200 and 250 for given data then calculate the coefficients Of skewness and kurtosis.
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of change of origin and scale both.
For the following distribution, calculate first four central moments using recurrence
relations. Also find the coefficients of skewness and kurtosis.
| Marks: | 2.7- 7.5 | 7.5- 12.5 | 12.5- 17.5 | 17.5- 22.5 | 22.5- 27.5 | 27.5- 32.5 | 32.5- 37.5 |
| Frequency: | 06 | 13 | 23 | 39 | 19 | 15 | 05 |
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variables X and Y. The marks of lo students of a class in Mathematics and Statistics are given below:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mathematics | 40 | 46 | 42 | 30 | 35 | 28 | 39 | 43 | 25 | 45 |
| Statistics | 35 | 41 | 36 | 32 | 42 | 48 | 29 | 38 | 28 | 40 |
If each value of X is multiplied by 10 and each value of Y is multiplied by 20, then the modified regression coefficient 
would be the half of previous.
What do you mean by measures of central tendency? Also find the missing frequency for the following frequency distribution if median is given 25:
Derive the formula for the coefficient of partial correlation coefficient R1.23, R2.13 and R3.12 for the following data:
| X1 | 10 | 20 | 30 | 40 | 50 |
| X2 | 20 | 30 | 40 | 50 | 60 |
| X3 | 30 | 40 | 50 | 60 | 70 |