Practice questions for the Midterm

In this assignment, you will serve as an expert consultant for MPHR. MPHR is interested in examining the descriptive statistics on a number of important employee characteristics including personality, job performance, and tenure. Using their dataset below, you will calculate descriptive statistics and provide your assessment of the results.

Dave Jackson, the HR Director has obtained data from a sample of employees at MPHR including personality scores on five facets of personality: neuroticism, extraversion, openness, agreeableness, and conscientious. Scores on these measures range from (1-100) with 100 indicating a higher standing on a particular personality trait. In addition, job performance data is available (one-seven scale as shown below) and tenure (in years).

Using Tab 1 of the MPHR Dataset download,( I have attached) the HR Director is interested in the following questions:

1. What is the mean for job performance ratings? Describe what this statistic tells us about performance at MPHR.

2. What is the mode for job performance ratings? Describe what this statistic tells us about performance at MPHR.

3. What is the mean and median for tenure? Describe what these statistics tell us about tenure at MPHR.

4. What are the standard deviations of extraversion and conscientiousness? Describe what these statistics tell us about these two variables in our sample.

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Here are the answers from students:

Student 1 answers:

1. What is the mean for job performance ratings? Describe what this statistic tells us about performance at MPHR.

The mean for job performance ratings is: 4.28. This is the average of all job performance ratings.

This tells us that in our sample, the average of job performance ratings hovers are 4.28, which meets expectations at MPHR. You can assume that half the sample size are receiving ratings less than 4.28 and the other half are receiving ratings higher than 4.28.

2. What is the mode for job performance ratings? Describe what this statistic tells us about performance at MPHR.

The mode for job performance ratings is: 6. This rating comes up the most often.

This tells us that 6 is the most common rating given for job performance. A 6 exceeds improvement, which tells us that most people are performing above average.

3. What is the mean and median for tenure? Describe what these statistics tell us about tenure at MPHR.

The mean for tenure is: 7.747 years

The median for tenure is: 4 years

The mean of 7.747 years tells us that the average time an employee spends at MPHR is 7.747 years. The median, which is the number found in the middle of the data set, tells us that most employees spend 4 years at MPHR. Because the mean and the median are different, you can assume that the data is slightly skewed. There are probably a few individuals that spent significantly more years at MPHR than the median amount, which might’ve skewed the mean.

4. What are the standard deviations of extraversion and conscientiousness? Describe what these statistics tell us about these two variables in our sample.

The standard deviation for Extraversion is: 27.98 or 28.

The standard deviation for Conscientiousness is: 22.28

The standard deviations for extraversion and conscientiousness are considered to be large. This indicates that the data is more spread out and there is more variation. A low standard deviation would be closer to the mean and show that there is little variation in the dataset examined.

Student 2 answers:

Mean Job Performance

Mean Job Performance: 4.28

The average job performance across the sample of 99 employees falls within the “meets expectations” rankings. While this average is a helpful reference point, it is possible that the mean score could be skewed by a few outliers. So, MPHR would need to keep this in mind.

Mode for Job Performance Ratings

Mode Job Performance: 6

Across the 99 employees sampled, 6 (exceeds improvement) is the most common performance rating. While there are a number of factors to consider in performance ratings (mean, motivations behind the scores, etc.), having a mode of 6 could be positive news for MPHR.

Mean and Median Tenure

Mean Tenure: 7.7 years

Median Tenure: 4 years

The mean tenure is 7.7 years. This is the average number of years employees have at the company. However, this number may be skewed by a few outliers, particularly a few employees who have been with MPHR 25+ years.

On the other hand, the median tenure is just 4 years. This median figure gives a sense of what most employees experience. In other words, most employees generally spend around 4 years at the company.

Standard Deviations for Extraversion and Conscientiousness

Extraversion standard deviation = 27.98 (Average of extraversion = 43.86)

Conscientiousness standard deviation = 22.28 (Average of conscientiousness = 37.74)

In both cases, extraversion and conscientiousness, the standard deviations are fairly large (27.98 and 22.28 respectively). This means that there is significant variation or spread away from the average for both traits. This is important for MPHR to keep in mind when making observations and planning. The average for each trait is a reference point, but there is a lot of variability from that average across the majority of the employees. For example, in the case of extraversion, one end of the standard deviation could be 15.88 while the other end could be 71.84, and that’s just within one standard deviation in that trait. So, the large standard deviations for both traits means that there is great variability amongst the majority of the employees sampled.

Student 3 answers:

1. What is the mean for job performance ratings? Answer: 4.28

The mean is a measure of central tendency, and it is better known as the average. It is the sum of all the values in a distribution and divided by the number of values. The mean should be employed only in relation to interval/ratio variables, however, its not uncommon to see it being used for ordinal variables as well. The mean can also be vulnerable to outliers.

Describe what this statistic tells us about performance at MPHR.

The mean can tell us that from based on the sample of employees (99) the results indicated that employees had an average job performance rating of 4.28 and it falls within the “meets expectations” ranking. As mentioned in the definition before, there is vulnerability for outliers, so this is a piece of information that should not be overlooked.

1. What is the mode for job performance ratings? Answer: 6

The mode is the value that occurs most frequently in a distribution. And it can be employed in relation to all types of variables.

Describe what this statistic tells us about performance at MPHR.

The mode is indicating that the most frequent occurrence from the student sample was exceeded improvement, which tells us that since the employees are already exceeding improvement it is possible for them to continue improvement and reach exceptional or real strength. There is an opportunity at MPHR to engage further to see what is working and what could improve.

1. What is the mean and median for tenure? The mean for tenure is 7.75 years and the median for tenure is 4 years

The mean is a measure of central tendency, and it is better known as the average – sum all the values in a distribution and then divide by the number of values. The median is derived by arraying all the values in a distribution from the smallest to the largest and then finding the middle point.

Describe what these statistics tell us about tenure at MPHR.

The statistics regarding tenure indicate the average years that employees have continued to stay with the organization is 7.75. For the median in regard to tenure, it is only 4 and it is not impacted by outliers. The difference in these 2 statistics is that the mean can be affected by an outlier with longer tenure, then it affects the overall tenure statistics. The median might be a better representation of accurate tenure.

1. What are the standard deviations of extraversion and conscientiousness? Answer: The standard deviation of extraversion is 27.98 and the standard deviation of conscientiousness is 22.28.

The standard deviation is a measure of dispersion more specifically, it is the average amount of variation around the mean. The standard deviation is calculated by taking the difference between each value in a distribution and the mean and then dividing the total of the differences by the number of values. It is also affected by outliers, but their impact is offset by dividing by the number of values in the distribution.

Describe what these statistics tell us about these two variables in our sample.

When analyzing both statistics extraversion and conscientiousness, it appears that the standard deviation is high and there is a larger spread in each measure.

For more information on The Standard Deviation for Conscientiousness read this: https://en.wikipedia.org/wiki/Conscientiousness

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