The provided image shows a set of 17 college graduates' working hours and a box-and-whisker plot (also called a boxplot) based on those hours. Let's break this down step by step:

Data:

The reported hours are: $47, 56, 55, 51, 69, 59, 54, 61, 45, 37, 38, 58, 57, 59, 48, 66, 51$

Steps to Construct the Box-and-Whisker Plot:

1. Sort the data in ascending order: $37, 38, 45, 47, 48, 51, 51, 54, 55, 56, 57, 58, 59, 59, 61, 66, 69$

2. Find the five-number summary:

   • Minimum: 37
   • Lower Quartile (Q1): Median of the lower half of data $(37, 38, 45, 47, 48, 51, 51, 54)$: $Q1 = 47$
   • Median (Q2): Middle value of the sorted dataThe provided image shows a set of 17 college graduates' working hours and a box-and-whisker plot (also called a boxplot) based on those hours. Let's break this down step by step:

Data:

The reported hours are: $47, 56, 55, 51, 69, 59, 54, 61, 45, 37, 38, 58, 57, 59, 48, 66, 51$

Steps to Construct the Box-and-Whisker Plot:

1. Sort the data in ascending order: $37, 38, 45, 47, 48, 51, 51, 54, 55, 56, 57, 58, 59, 59, 61, 66, 69$

2. Find the five-number summary:

   • Minimum: 37
   • Lower Quartile (Q1): Median of the lower half of data $(37, 38, 45, 47, 48, 51, 51, 54)$: $Q1 = 47$
   • Median (Q2): Middle value of the sorted $Q2 = 55$
   • Upper Quartile (Q3): Median of the upper half of data $(56, 57, 58, 59, 59, 61, 66, 69)$: $Q3 = 59$
   • Maximum: 69

3. Plot the box:

   • The box spans from $Q1 = 47$ to $Q3 = 59$ with a line at the median $Q2 = 55$.
   • The whiskers extend from the minimum value (37) to the maximum value (69).

4. Outliers: No outliers are shown in this dataset, meaning no values fall outside 1.5 times the interquartile range (IQR).

Thus, the box-and-whisker plot is a visual representation of this five-number summary, as seen in the provided image.

Would you like a more detailed explanation of any of these steps?

Relative Questions:

1. How do you calculate quartiles for a dataset?
2. What is the interquartile range (IQR), and how is it useful?
3. How do you determine if a data point is an outlier using a boxplot?
4. What is the difference between a boxplot and a histogram?
5. How would a skewed dataset affect the shape of a boxplot?

Tip: When analyzing data, always check for outliers as they can skew the results and provide insights into anomalies in the data.