Answer:
To answer your question, you need to analyze the dot plot and find the mean, median, mode, and range of the data. Here are the steps to do that:
- The mean is the average of all the data values. To find the mean, you need to add up all the data values and divide by the number of data points. In this case, there are 20 data points, so you need to add up all the dots on the graph and divide by 20. You can use a calculator to do this, or you can estimate by using the midpoints of each interval. For example, the midpoint of the interval 5-10 is 7.5, so you can count 2 dots in that interval as 2 x 7.5 = 15. If you do this for all the intervals, you get:
(2 x 7.5) + (3 x 12.5) + (4 x 17.5) + (3 x 22.5) + (4 x 27.5) + (2 x 32.5) + (1 x 37.5) + (1 x 42.5) = 480
Then, divide by 20 to get the mean:
480 / 20 = 24
So, the mean commute time is about **24 minutes**.
- The median is the middle value of the data when it is arranged in order. To find the median, you need to count how many data points are below and above the median. Since there are an even number of data points (20), the median will be between the 10th and 11th values. To find these values, you need to start from either end of the graph and count until you reach the middle. For example, starting from the left end, you can count:
5, 10, 10, 15, 15, 15, 20, 20, 20, **20**, **25**, 25, 25, 25, 30, 30, 35, 40, 40, 45
The bolded values are the 10th and 11th values. To find the median, you need to take their average:
(20 + 25) / 2 = 22.5
So, the median commute time is **22.5 minutes**.
- The mode is the most frequent value of the data. To find the mode, you need to look at which interval has the most dots on the graph. In this case, it is the interval **25-30**, which has **4 dots**. So, the mode commute time is **between 25 and 30 minutes**.
- The range is the difference between the maximum and minimum values of the data. To find the range, you need to look at which values are at the ends of the graph. In this case, they are **5** and **45**. So, to find the range, you need to subtract:
45 - 5 = **40**
So, the range of commute times is **40 minutes**.