each year, a magazine compiles a list of the 400 richest people in a country. as of 2008, the top 10 on the…

each year, a magazine compiles a list of the 400 richest people in a country. as of 2008, the top 10 on the list are as shown in the table below. person wealth ($billions) a b c d e f g h i j 51.5 48.7 48.1 34.5 31.2 30.3 30.3 27.9 19.7 19.7 a. find the mean. b. find the median. c. find the mode. a. the mean is $□ billion. (type an integer or a decimal.) b. the median is $□ billion. (type an integer or a decimal.) c. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mode is $□ billion. (type an integer or a decimal.) b. the modes are $□ billion. (type an integer or a decimal. use a comma to separate answers as needed.) c. the data set has no mode.

each year, a magazine compiles a list of the 400 richest people in a country. as of 2008, the top 10 on the list are as shown in the table below. person wealth ($billions) a b c d e f g h i j 51.5 48.7 48.1 34.5 31.2 30.3 30.3 27.9 19.7 19.7 a. find the mean. b. find the median. c. find the mode. a. the mean is $□ billion. (type an integer or a decimal.) b. the median is $□ billion. (type an integer or a decimal.) c. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mode is $□ billion. (type an integer or a decimal.) b. the modes are $□ billion. (type an integer or a decimal. use a comma to separate answers as needed.) c. the data set has no mode.

Answer

Explanation:

Step1: Calculate the sum of data

$51.5 + 48.7+48.1 + 34.5+31.2+30.3+30.3+27.9+19.7+19.7=342.9$

Step2: Calculate the mean

The number of data points $n = 10$. Mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{342.9}{10}=34.29$

Step3: Arrange data in ascending order

$19.7,19.7,27.9,30.3,30.3,31.2,34.5,48.1,48.7,51.5$

Step4: Calculate the median

Since $n = 10$ (even), median $M=\frac{\frac{n}{2}^{th}\text{ value}+\left(\frac{n}{2}+1\right)^{th}\text{ value}}{2}=\frac{30.3 + 31.2}{2}=30.75$

Step5: Find the mode

The mode is the value that appears most frequently. Here, $19.7$ and $30.3$ both appear twice.

Answer:

a. $34.29$ b. $30.75$ c. B. The modes are $19.7,30.3$ billion.