Drag the tiles to the correct boxes to complete the pairs.
The owner of a real estate agency is looking over the monthly commission earned by the top three brokers in the past month. She has calculated the mean and standard deviation, SD, of their commissions, in dollars, as shown below.
Match each broker with the correct description.
Benjamin
Cathy
Amanda
Answer (2)
Benjamin has the lowest mean commission and a relatively high standard deviation.
Cathy has the highest mean commission and the highest standard deviation.
Amanda has a mean commission between Benjamin and Cathy, and the lowest standard deviation.
Therefore, the matches are: Benjamin -> Lower average sales, but more variable than Amanda; Cathy -> Higher average sales, and more variable than the others; Amanda -> Average sales are good, but the least variable.
Explanation
Analyze the data We are given the mean and standard deviation of the monthly commissions earned by three brokers: Amanda, Benjamin, and Cathy.
Amanda: Mean = $75,463.12, SD = $3,839.02 Benjamin: Mean = $74,124.87, SD = $4,062.50 Cathy: Mean = $76,095.71, SD = $4,227.54
Compare means and standard deviations Let's compare the means of the three brokers to determine who has the highest and lowest average commission.
Cathy has the highest mean commission ($76,095.71), followed by Amanda ($75,463.12), and then Benjamin ($74,124.87). Now, let's compare the standard deviations of the three brokers to determine who has the most and least variability in their commission. Cathy has the highest standard deviation ($4,227.54), followed by Benjamin ($4,062.50), and then Amanda ($3,839.02).
Match brokers to descriptions Based on the comparisons of means and standard deviations, we can match each broker to a description that accurately reflects their performance.
Benjamin: Has the lowest mean commission and a relatively high standard deviation. Cathy: Has the highest mean commission and the highest standard deviation. Amanda: Has a mean commission between Benjamin and Cathy, and the lowest standard deviation.
Final Answer Benjamin: Lower average sales, but more variable than Amanda. Cathy: Higher average sales, and more variable than the others. Amanda: Average sales are good, but the least variable.
Examples
Understanding the mean and standard deviation of sales commissions can help a real estate agency owner identify top performers, those who might need additional training, and those with consistent performance. For example, a broker with a high mean and low standard deviation consistently performs well, while a broker with a low mean and high standard deviation may need help improving their sales strategies. This analysis can also help in setting realistic sales targets and designing effective incentive programs.
In analyzing the commissions of brokers Benjamin, Cathy, and Amanda, Cathy has the highest commission and variability, Benjamin has the lowest commission and is more variable, while Amanda has a middle commission with the least variability. Their performance is summarized based on these metrics. This analysis helps identify which broker performs consistently versus those with fluctuating sales.
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