Question

carson has 9 tomato plants. he counts the number of tomatoes on each plant. the data he collects ar listed below from least to greatest. make a box plot to show carsons data. plot a point for the minimum, maximum, median, lower quartile, and upper quartile to create the box plot. carsons plants number of tomatoes

Explanation:

Step1: Identify the minimum value

The minimum value (min) is \(0\).

Step2: Identify the first quartile (Q1)

For a data set with \(n = 9\) values, the first quartile is the \(\frac{n + 1}{4}\)th value. \(\frac{9+ 1}{4}=2.5\)th value. Using linear - interpolation between the 2nd and 3rd values. The 2nd value is \(2\) and the 3rd value is \(2\), so \(Q1 = 2\).

Step3: Identify the median

The median is the \(\frac{n + 1}{2}\)th value. \(\frac{9+1}{2}=5\)th value. The 5th value is \(2\).

Step4: Identify the third quartile (Q3)

The third quartile is the \(\frac{3(n + 1)}{4}\)th value. \(\frac{3(9 + 1)}{4}=7.5\)th value. Using linear - interpolation between the 7th and 8th values. The 7th value is \(6\) and the 8th value is \(6.5\), so \(Q3=\frac{6 + 6.5}{2}=6.25\).

Step5: Identify the maximum value

The maximum value (max) is \(7\).

Answer:

Plot points at \(0\) (min), \(2\) (Q1), \(2\) (median), \(6.25\) (Q3), and \(7\) (max) on the number line and then draw the box plot with a box from \(Q1 = 2\) to \(Q3=6.25\), a line inside the box at the median \(2\), and whiskers from the box to the min \(0\) and max \(7\).