Box-and-whiskers, algebra

Question

Construct a box-and-whisker plot of the following numbers:

70, 55, 43, 66, 32, 35, 48, 68, 69, 39, 31, 52

Answer 1

Hello, thank you for taking the time to post your question!

We can compute the five-number summary based on the information given in the question.

Minimum: 31

Q1: 37

Median: 50

Q3: 67

Maximum: 70

It won’t let me put the image in here directly but I would use technology like SPSS or an online calculator in order to form the actual plot so that you get a nice clean image.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

To construct a box-and-whisker plot, we need to find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values of the data set. Then we can represent these values graphically.

First, let's sort the numbers in ascending order:

31, 32, 35, 39, 43, 48, 52, 55, 66, 68, 69, 70

Now, we can find the quartiles:

Q1: The median of the lower half of the data set.

Q2: The median of the entire data set.

Q3: The median of the upper half of the data set.

Q1: 39

Q2: 52.5

Q3: 67

Next, we find the minimum and maximum values:

Minimum: 31

Maximum: 70

Now, we can construct the box-and-whisker plot using these values:

| * |

| * |

| * |

------|----------------|------

| |

31 39 52.5 67 70

In the plot, the asterisks (*) represent the quartiles (Q1, Q2, Q3), the vertical line on the left represents the minimum value, and the vertical line on the right represents the maximum value. The box represents the interquartile range (Q3 - Q1), and the horizontal line within the box represents the median.

Therefore, the constructed box-and-whisker plot for the given numbers is shown above.