A business researcher has to decide which of three employees should be placed in a particular job that requires a high level of perceptual-motor coordination. All three employees have taken tests of perceptual-motor coordination, but each took a different test.
Employee A scored 15 on a test with a mean of 10 and a standard deviation of 2.
Employee B scored 350 on a test with a mean of 300 and a standard deviation of 40.
Employee C scored 108 on a test with a mean of 100 and a standard deviation of 16.
On all three tests, higher scores mean greater coordination.
Which employee has the best perceptual–motor coordination?
Z = (score-mean)/SD
Which has the highest Z score?
To determine which employee has the best perceptual-motor coordination, we need to compare their scores relative to the mean and standard deviation of their respective tests.
Let's calculate the z-scores for each employee using the formula: z = (x - mean) / standard deviation.
For Employee A:
z_A = (15 - 10) / 2 = 2.5 / 2 = 1.25
For Employee B:
z_B = (350 - 300) / 40 = 50 / 40 = 1.25
For Employee C:
z_C = (108 - 100) / 16 = 8 / 16 = 0.5
The z-score tells us how many standard deviations each employee's score is from the mean. The higher the z-score, the better their perceptual-motor coordination compared to others who took the test.
Since both Employee A and Employee B have a z-score of 1.25, it means they performed equally well on their respective tests and have the same level of perceptual-motor coordination. Employee C has a lower z-score of 0.5, indicating a slightly lower level of perceptual-motor coordination.
Therefore, based on the scores and z-scores, it can be concluded that either Employee A or Employee B has the best perceptual-motor coordination, as they performed equally well on their respective tests.
To determine which employee has the best perceptual-motor coordination, we need to compare their scores relative to the mean and standard deviation of their respective tests. The concept we will use is called z-scores.
The formula for calculating a z-score is:
z = (x - mean) / standard deviation
Let's calculate the z-scores for each employee:
For Employee A:
z_A = (15 - 10) / 2
= 5 / 2
= 2.5
For Employee B:
z_B = (350 - 300) / 40
= 50 / 40
= 1.25
For Employee C:
z_C = (108 - 100) / 16
= 8 / 16
= 0.5
Now that we have the z-scores, we can compare them. A higher z-score indicates a higher relative performance compared to the test's mean and standard deviation.
Employee A has a z-score of 2.5, which means their score is 2.5 standard deviations above the mean. This indicates a relatively high performance.
Employee B has a z-score of 1.25, which means their score is 1.25 standard deviations above the mean. This also indicates a relatively high performance, but slightly lower than Employee A.
Employee C has a z-score of 0.5, which means their score is 0.5 standard deviations above the mean. This indicates a lower performance compared to the other two employees.
Therefore, based on their z-scores, Employee A has the best perceptual-motor coordination among the three employees.