Hourly Earnings Refer to the data set in Exercise 26 and the box-and-whisker plot you drew that represents the data set.


b. What percent of the employees made more than \$23.39 per hour?

Verified step by step guidance

1. Step 1: Recall that a box-and-whisker plot divides the data into quartiles, with the box representing the interquartile range (IQR) and the whiskers extending to the minimum and maximum values. Identify the position of \$23.39 on the plot relative to the quartiles.
2. Step 2: Determine which quartile \$23.39 falls into. If it is above the third quartile (Q3), then it represents the upper 25% of the data. If it is within the IQR, calculate its position relative to Q3.
3. Step 3: Use the cumulative percentage of the quartiles to estimate the percentage of employees earning more than \$23.39. For example, if \$23.39 is above Q3, then the percentage of employees earning more than \$23.39 is less than 25%.
4. Step 4: If \$23.39 is within the IQR, calculate the proportion of the data in the upper quartile that exceeds \$23.39. This can be done by determining the relative position of \$23.39 within the range of Q3 to the maximum value.
5. Step 5: Combine the results from the previous steps to express the percentage of employees earning more than \$23.39 as a proportion of the total data set.

Key Concepts

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation of a data set that displays its minimum, first quartile, median, third quartile, and maximum. It helps visualize the distribution and identify outliers. The box represents the interquartile range (IQR), while the 'whiskers' extend to the smallest and largest values within 1.5 times the IQR from the quartiles.

Percentile

A percentile is a measure used in statistics to indicate the value below which a given percentage of observations fall. For example, the 75th percentile means that 75% of the data points are below that value. Understanding percentiles is crucial for interpreting data distributions and determining how a specific value compares to the rest of the data set.

Calculating Percentages

Calculating percentages involves determining the proportion of a part relative to the whole, expressed as a fraction of 100. In the context of the question, to find the percentage of employees earning more than a specific hourly rate, one would count the number of employees above that rate and divide by the total number of employees, then multiply by 100 to convert it to a percentage.