Question

Fine the five number summary for the data set (3,5,7,8,12,14,21,13,18)and construct a box plot.​

Answer 1

To find the five number summary of the data set (3,5,7,8,12,14,21,13,18), order the data, identify the min, max, median, first quartile, and third quartile. Calculate the interquartile range (IQR) and check for potential outliers. There are none in this set, so you can construct a box plot using the five-number summary.

Step-by-step explanation:

To find the five number summary of the given data set (3,5,7,8,12,14,21,13,18), and to construct a box plot, follow these steps:

1. Order the data set from smallest to largest: (3, 5, 7, 8, 12, 13, 14, 18, 21).
2. Identify the minimum (3) and maximum (21) values.
3. The median (second quartile, Q2) is the middle number when the data set is ordered, which is 12 in this case.
4. The first quartile (Q1) is the median of the first half of the data, which is 7.
5. The third quartile (Q3) is the median of the second half of the data, which is 14.
6. With these values, we have the five-number summary: Min = 3, Q1 = 7, Median = 12, Q3 = 14, Max = 21.
7. To calculate the interquartile range (IQR), subtract Q1 from Q3: IQR = Q3 - Q1 = 14 - 7 = 7.
8. To determine outliers, calculate Q1 - 1.5(IQR) and Q3 + 1.5(IQR). Any data points outside of these ranges would be considered potential outliers. For this data set, there are no values less than Q1 - 1.5(IQR) = 7 - 1.5(7) = -3.5 or greater than Q3 + 1.5(IQR) = 14 + 1.5(7) = 24.5, so there are no potential outliers.
9. To construct the box plot, draw a scale, plot the points of the five number summary, and draw rectangles and lines to represent these values.
10. As no actual construction cannot be drawn here, these instructions will guide you in plotting it on your paper.