Question

practice problems 5 problems 1 the dot plot displays the number of bushes in the yards for houses in a neighborhood. what is the median? number of bushes 2 the data set represents the shoe sizes of 19 students in a fifth - grade physical education class. 4 5 5 5 6 6 6 6 7 7 7 7 7.5 7.5 8 8 8.5 8.5 9 create a box plot to represent the distribution of the data.

Explanation:

Step1: Count total data points for dot - plot

Count the number of dots in the dot - plot. There are \(2 + 3+4 + 3+2 + 1+5=20\) data points.

Step2: Find position of median for dot - plot

Since \(n = 20\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data values. \(\frac{n}{2}=10\) and \(\frac{n}{2}+1 = 11\).

Step3: Determine median for dot - plot

Counting the dots in order, the 10th and 11th ordered values fall on 7. So the median is \(\frac{7 + 7}{2}=7\).

For the box - plot:

Step1: Order the data set

The ordered data set is \(4,5,5,5,6,6,6,6,7,7,7,7,7.5,7.5,8,8,8.5,8.5,9\).

Step2: Find the median (Q2)

Since \(n = 19\) (an odd number), the median (Q2) is the \(\frac{n + 1}{2}=\frac{19+1}{2}=10\)th value, which is 7.

Step3: Find the lower half and Q1

The lower half of the data is \(4,5,5,5,6,6,6,6,7\). Since \(n_1=9\) (odd), Q1 is the \(\frac{9 + 1}{2}=5\)th value, which is 6.

Step4: Find the upper half and Q3

The upper half of the data is \(7.5,7.5,8,8,8.5,8.5,9\). Since \(n_2 = 9\) (odd), Q3 is the \(\frac{9+1}{2}=5\)th value of the upper - half, which is 8.

Step5: Identify the minimum and maximum

The minimum value is 4 and the maximum value is 9.

To draw the box - plot:

• Draw a number line that includes the range from 4 to 9.
• Mark a point at the minimum (4), Q1 (6), Q2 (7), Q3 (8), and the maximum (9).
• Draw a box from Q1 to Q3 with a vertical line inside the box at Q2.
• Draw whiskers from the box to the minimum and maximum values.

Answer:

1. The median for the dot - plot is 7.
2. To create the box - plot: Mark minimum = 4, Q1 = 6, Q2 = 7, Q3 = 8, maximum = 9. Draw a box from Q1 to Q3 with a line at Q2 and whiskers to the minimum and maximum.