Kite ABCD is translated (x − 2, y + 3) and then rotated 90° about the origin in the counterclockwise direction. Complete the table to show the locations of A″, B″, C″, and D″ after both transformations. -A″ (4, 7), B″ (5, 4), C″ (4, 3), D″ (3, 4)

- A″ (−3, −4), B″ (−4, −7), C″ (−5, −4), D″ (−4, −3)

- A″ (−4, −7), B″ (−5, −4), C″ (−4, −3), D″ (−3, −4)

- A″ (−7, 4), B″ (−4, 5), C″ (−3, 4), D″ (−4, 3)

Range

The range measures the spread of the dataset by calculating the difference between the largest and the smallest element. In your case, marks range from 6 to 10, so the range is 10-6=4.

How many students

The frequency tells you how many students got each mark. So, we know that 5 students got a mark of 6, 4 students got a mark of 7, 7 students got a mark of 8, 10 students got a mark of 9, 4 students got a mark of 10.

This implies that, in total, we have

students.

Mean

The mean is given by the sum of the marks, divided by the number of students. We already observed how many students got each mark, so the sum of all marks will be a weighted sum, where each mark counts once per student:

Now we divide this sum by the number of students to get

So, the average mark is about 8.