Mean Median from Density Curves

Identify the mean and median on the density curves on the left:

• (a) The mean is at point B, the median is at point A.

  (b) The mean and median are both at point B.

  (c) The mean is at point A, the median is at point B.

• (a) The mean is at point C, the median is at point B.

  (b) The mean and median are both at point A.

  (c) The mean is at point A, the median is at point B.

• (a) The mean is at point A, the median is at point B.

  (b) The mean and median are both at point C.

  (c) The mean is at point B, the median is at point A.

• (a) The mean is at point C, the median is at point A.

  (b) The mean and median are both at point C.

  (c) The mean is at point C, the median is at point A.

The mean on a density curve is...

• a. when you take each of the possible values and you weigh it by their frequencies, and you add all of that up

• b. the balancing point

• c. the weighted average of all of possible values

• a and c

• all of the above

How can you identify the mean and median of a density curve?

Sketch a density curve that is symmetric, but has a shape different from that of the curve in the image below:

• A

• B

• C

• D

• E

For the density curve shown, which statement is true?

• The mean is greater than the median.

• The mean is less than the median.

• The mean and median are equal.

• The mean could be either greater than or less than the median.

• None of the above is correct.

Non-symmetric distributions where the mean is varying from the median are referred to as being skewed.

• True

• False

For the density curve shown, which statement is true?

• The mean and median are equal.

• The mean is greater than the median.

• The mean is less than the median

• The mean could be either greater than or less than the median.

• None of the above is correct

Which of the following properties is true for all Normal density curves? I. They are symmetric. II. The curve reaches its peak at the mean. III. 95% percent of the area under the curve is within one standard deviation of the mean.

• I only

• II only

• I and II only

• I and III only

• All three statements are correct

How much area is beyond two standard deviations from the mean under a normal distribution?

• ≈ 16%

• ≈ 8%

• ≈ 32%

• ≈ 5%