QuestionGiven salaries of 30 employees, identify measures of central tendency: a) for proving underpayment, b) for proving fair pay, c) fairest measure.
Studdy Solution
STEP 1
Assumptions1. The data provided represents the annual salaries of30 employees in a factory.
. We are asked to consider which measures of central tendency (mean, median, mode) would be used by different parties to argue for their perspective on the salaries.
3. We assume that the labor representative would want to show that the salaries are low, while the owners would want to show that the salaries are high.
4. We also need to consider which measure of central tendency represents the data most fairly.
STEP 2
First, let's calculate the mean of the salaries. The mean is calculated by summing all the values and dividing by the number of values.
STEP 3
Now, plug in the given values for the salaries and number of salaries to calculate the mean.
STEP 4
Calculate the mean salary.
STEP 5
Next, let's calculate the median of the salaries. The median is the middle value when the values are arranged in ascending order. Since we have30 values, the median will be the average of the15th and16th values.
STEP 6
Looking at the data, we can see that the15th and16th values are both \$
STEP 7
Finally, let's find the mode of the salaries. The mode is the value that appears most frequently in the data set. Looking at the data, we can see that the most frequent salary is \$15,000.
STEP 8
a) A labor representative would likely use the mode to argue that workers are underpaid, as it is the lowest of the three measures of central tendency and represents the most common salary.
b) The owners would likely use the mean to argue that workers are well paid, as it is the highest of the three measures and is influenced by the high salary of \$150,000.
c) The median seems to represent the data most fairly, as it is not influenced by the extreme values and represents the middle salary.
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