Question

1. the dot - plot displays the number of bushes in the yards for houses in a neighborhood. state the mode and median of this data. response: mode = median = number of bushes

Explanation:

Step1: Recall mode definition

The mode is the value that appears most frequently in a data - set.

Step2: Count dot frequencies

From the dot - plot, the number 7 has 5 dots, the number 11 has 5 dots, and other numbers have fewer dots. So the modes are 7 and 11.

Step3: Recall median definition

The median is the middle value when the data is arranged in ascending or descending order. First, find the total number of data points. Counting the dots: \(2 + 3+5 + 4+2+1+5=22\) data points.

Step4: Calculate median position

Since \(n = 22\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data values. \(\frac{n}{2}=11\) and \(\frac{n}{2}+1 = 12\).

Step5: Arrange data and find median

Arrange the data in ascending order. Counting the dots from the lowest value, the 11th and 12th values are both 8. So the median is \(\frac{8 + 8}{2}=8\).

Answer:

Mode = 7, 11
Median = 8