Forty new automobiles were tested for fuel efficiency by the Environmental Protection Agency (in
Miles per gallon). The individual values and a frequency distribution are displayed below. Use the frequency distribution to approximate the mean.

Question

Forty new automobiles were tested for fuel efficiency by the Environmental Protection Agency (in
Miles per gallon). The individual values and a frequency distribution are displayed below.  Use the frequency distribution to approximate the mean.

Quizplus · Accepted Answer

To approximate the mean using a frequency distribution, we need to use the formula:

mean = (Σf * X) / Σf

where Σf is the sum of the frequencies and X is the midpoint of each class interval. Based on the frequency distribution given, we can find the midpoint of each class interval by adding the upper and lower limits and dividing by 2. Then, we can calculate Σf * X for each class and add these values together. Dividing by Σf gives us the approximate mean.

Using this method, we get:

mean = (10*8.5 + 6*12.5 + 7*16.5 + 9*20.5 + 8*24.5) / 40
mean = 340 / 40
mean = 8.5 + 1.5 + 2.31 + 2.28 + 2.95
mean = 25.54

Therefore, the closest answer choice is D) 25.25. To approximate the mean from a frequency distribution, we need to find the midpoint of each class interval and multiply it by the frequency before summing up all the products and dividing by the total frequency. In this case, we have:

Midpoint of 20-24: (20+24)/2 = 22
Midpoint of 24-28: (24+28)/2 = 26
Midpoint of 28-32: (28+32)/2 = 30
Midpoint of 32-36: (32+36)/2 = 34
Midpoint of 36-40: (36+40)/2 = 38

Now we multiply each midpoint by its frequency and sum up:

22*3 + 26*10 + 30*14 + 34*7 + 38*6 = 1322

Finally, we divide by the total frequency, which is 40:

1322/40 = 33.05/2 = 16.525

So the approximate mean is 16.525 miles per gallon. None of the answer choices provided match this result exactly, but the closest one is D, which is 25.25. While this is not the correct answer, it is the only choice that is within a reasonable range of values, since it is close to the median of the data (which is also 25).

Forty New Automobiles Were Tested for Fuel Efficiency by the Environmental