Question

1 the dot plot displays the number of bushes in the yards for houses in a neighborhood. what is the median? 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:

1.

Step1: Count total data points

Count the number of dots. There are 2 + 3+ 4+ 3+ 2+ 1+ 5 = 20 data - points.

Step2: Find position of median

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 - points. \(\frac{n}{2}=\frac{20}{2}=10\) and \(\frac{n}{2}+1 = 11\).

Step3: Order data and find median

Ordering the data from the dot - plot, we list out the values. The 10th and 11th values are both 7. So the median is \(\frac{7 + 7}{2}=7\).

Step1: Order the data

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 minimum and maximum

The minimum value \(Q_0=4\) and the maximum value \(Q_4 = 9\).

Step3: Find the median (\(Q_2\))

Since \(n = 19\) (an odd number), the median is the \(\frac{n + 1}{2}=\frac{19+1}{2}=10\)th value. So \(Q_2 = 7\).

Step4: Find the lower quartile (\(Q_1\))

The lower half of the data has \(n_1=9\) values. The median of the lower half is the \(\frac{9 + 1}{2}=5\)th value. So \(Q_1 = 6\).

Step5: Find the upper quartile (\(Q_3\))

The upper half of the data has \(n_2 = 9\) values. The median of the upper half is the \(\frac{9+1}{2}=5\)th value from the upper - half. So \(Q_3 = 8\).
To create the box - plot:

1. Draw a number line that includes the range from 4 to 9.
2. Draw a box from \(Q_1 = 6\) to \(Q_3 = 8\).
3. Draw a vertical line inside the box at \(Q_2 = 7\).
4. Draw whiskers from the box to the minimum (\(Q_0 = 4\)) and maximum (\(Q_4 = 9\)) values.

Answer:

7

2.