Below are numbers of hours that a sample of 16 college graduates reported working last week.
\[
65,47,46,42,69,55,56,35,58,68,52,57,48,45,49,52
\]
Send data to calculator
Using the tool provided, construct a box-and-whisker plot (sometimes called a boxplot) for the data.
Answer
\(\boxed{Final Answer:}\) The box-and-whisker plot shows that the minimum number of hours worked is 35, the first quartile (Q1) is 46.75, the median (Q2) is 52.0, the third quartile (Q3) is 57.25, and the maximum number of hours worked is 69.
Step 1 ：First, we need to calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of the data. These values will form the 'box' and 'whiskers' of the plot.
Step 2 ：The data given is: \(65, 47, 46, 42, 69, 55, 56, 35, 58, 68, 52, 57, 48, 45, 49, 52\)
Step 3 ：From this data, we calculate the following values: \(Q1 = 46.75\), \(Q2 = 52.0\), \(Q3 = 57.25\), \(min\_val = 35\), \(max\_val = 69\)
Step 4 ：We can now construct a box-and-whisker plot using these values. The box represents the interquartile range (from Q1 to Q3), and the whiskers represent the range of the data (from min to max).
Step 5 ：The median line in the box shows that half of the graduates worked less than or equal to 52 hours, and half worked more.
Step 6 ：The plot also shows that the data is slightly skewed to the right, meaning that there are some graduates who worked significantly more hours than most others.
Step 7 ：\(\boxed{Final Answer:}\) The box-and-whisker plot shows that the minimum number of hours worked is 35, the first quartile (Q1) is 46.75, the median (Q2) is 52.0, the third quartile (Q3) is 57.25, and the maximum number of hours worked is 69.
