One store mgr. $30
two assistant mgr. $20
Ten salespeople. $6
In the monthly store newsletter, the storeowner boasted, "My average employee earns $10.00 an hour!" Is her statement misleading?
Use the measures of central tendency (mean, median, and mode) to justify your answer.
We'll be happy to critique your answer.
i need help with my math homework
To determine whether the storeowner's statement is misleading or not, we need to calculate the measures of central tendency (mean, median, and mode) using the given salaries of the store's employees ($30 for the store manager, $20 for each assistant manager, and $6 for each salesperson).
1. Mean:
To calculate the mean, we need to find the sum of all the salaries and divide it by the total number of employees. Let's calculate it step by step:
Store Manager: $30
Assistant Managers: 2 x $20 = $40
Salespeople: 10 x $6 = $60
Total: $30 + $40 + $60 = $130
Now, let's calculate the mean:
Mean = Total / Number of employees
Mean = $130 / (1 + 2 + 10)
Mean = $130 / 13
Mean ≈ $10.00
The mean salary per hour for all employees is approximately $10.00, which aligns with the storeowner's statement. However, let's also calculate the median and mode to further analyze.
2. Median:
To calculate the median, we need to arrange the salaries in ascending order:
$6, $6, $6, $6, $6, $6, $6, $6, $6, $6, $20, $20, $30
Since there are 13 salaries, the median will be the middle value. In this case, there are two middle values, $6 and $6. Therefore, the median is $6.00.
3. Mode:
To calculate the mode, we need to find the salary that appears most frequently. In this case, the salary of $6 appears 10 times, while all other salaries appear only once. Therefore, the mode is $6.
Conclusion:
Based on the calculations of the mean, median, and mode, we can conclude that the storeowner's statement is misleading. Although the mean salary is $10.00, the median and mode salaries are much lower at $6.00. The mean is affected by the higher salary of the store manager and assistant managers, while the majority of employees, the salespeople, earn a lower salary. This distribution of salaries indicates that the average salary is being skewed by higher-paying positions, making the storeowner's statement misleading.