Question

listed below are the highest amounts of net worth (in millions of dollars) of all celebrities. 255, 200, 185, 175, 165, 165, 145, 145, 145, 145. a. find the mean. the mean is $\square$ million. (type an integer or a decimal rounded to one decimal place as needed.) b. find the median. the median is $\square$ million. (type an integer or a decimal rounded to one decimal place as needed.) c. find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mode(s) is(are) $\square$ million. (type an integer or a decimal. do not round. use a comma to separate answers as needed.) b. there is no mode.

Explanation:

Part a: Find the mean

Step 1: Sum the values

The data set is \( 255, 200, 185, 175, 165, 165, 145, 145, 145, 145 \).
Sum \( = 255 + 200 + 185 + 175 + 165 + 165 + 145 + 145 + 145 + 145 \)
\( = 255 + 200 = 455 \); \( 455 + 185 = 640 \); \( 640 + 175 = 815 \); \( 815 + 165 = 980 \); \( 980 + 165 = 1145 \); \( 1145 + 145 = 1290 \); \( 1290 + 145 = 1435 \); \( 1435 + 145 = 1580 \); \( 1580 + 145 = 1725 \).

Step 2: Divide by number of values

There are \( n = 10 \) values.
Mean \( = \frac{1725}{10} = 172.5 \).

Step 1: Order the data (already ordered: \( 145, 145, 145, 145, 165, 165, 175, 185, 200, 255 \))

Step 2: Find the middle (even \( n = 10 \), average of 5th and 6th terms)

5th term: \( 165 \); 6th term: \( 165 \).
Median \( = \frac{165 + 165}{2} = 165 \).

The mode is the most frequent value. \( 145 \) appears 4 times (more than any other value: \( 165 \) appears 2 times, others once).

Answer:

The mean is \( \$172.5 \) million.

Part b: Find the median