Q 3.23. - Elementary Statistics

Question

Find the 

a. Mean    b. median      c. mode

For the mean and the median, round each answer to one more decimal place than that used for the observations.

Billionaires' Club. Each year, Forbes magazine compiles a list of the $400$richest Americans. As of September $19, 2012$, the top 10 on the list are as shown in the following table.

Step-by-Step Solution

Answer

$$\begin{gathered} a)\$34.71 billions \\ b)\$29.45 billions \\ c) \$31.0 billions \end{gathered}$$

Step 1. Given information.

We have given data: $66.0, 46.0, 41.0, 31.0, 31.0, 27.9,26.8, 26.3, 26.1, 25.0$

Step 2. Mean of the data.

Mean$=\frac{Sum of observation }{Number of observation}$

$$\begin{gathered} =\frac{66.0+46.0+41.0+31.0+31.0+27.9+26.8+26.3+26.1+25.0 }{10} \\ =\frac{347.1}{10} \\ =34.71 \end{gathered}$$

Step 3. Median of the data.

Arrange the data in increasing order : $25.0, 26.1, 26.3, 26.8, 27.9, 31.0, 31.0, 41.0, 46.0, 66.0$

 Median

$$\begin{gathered} =\frac{5th +6th}{2} \\ =\frac{27.9+31.0}{2} \\ =\frac{58.9}{2} \\ =29.45 \end{gathered}$$ 

Step 4. Mode of the data.

The greatest frequency is the mode of the data set. 

The mode of the given data set is $31.0$