Question

The Fan Cost Index​ (FCI) is a measure of how much it costs a family of four to attend a major league baseball game.

The frequency distribution and the histogram for the Fan Cost Index are given below:

FCI​ (Dollars)	Frequency
​100-149.99	2
​150-199.99	0
​200-249.99	1
​250-299.99	1
​300-349.99	9
​350-399.99	12
​400-449.99	5

(a) Determine the shape of the distribution.

A. Right Skewed

B. Left Skewed

C. Normal

D. Uniform

​

(b) Determine if the mean or the median would be a better measure of center for this distrubution. If the mean is​ better, calculate the value. If the median is​ better, give the midpoint of the interval that contains it.

Select the correct choice below and fill in the answer box to complete your choice.

A. The median is a better measure of center for this distribution.

The midpoint of the interval that contains the median is $_______.

B. The mean is a better measure of center for this distribution.

The value of the mean is $_______.

Answer 1

(a) Determine the shape of the distribution.

Since the higher numerical values have higher frequencies, the distribution is left skewed. Hence the correct option is ,

B. Left Skewed

(b) Determine if the mean or the median would be a better measure of center for this distrubution. If the mean is​ better, calculate the value. If the median is​ better, give the midpoint of the interval that contains it.

Mean is affected by the skewness in distribution but median is not affected. Therefore we will use median as the center of distribution. Since the total frequency is 30(=2+0+1+1+9+12+5), we will find the 15th and 16th frequencies from the lowest value to get the value of median. This value lies in the interval ​350-399.99. The midpoint of the interval is (350+399.99)/2 = 375

A. The median is a better measure of center for this distribution.

The midpoint of the interval that contains the median is $375.