Question

find the (a) mean, (b) median, (c) mode, and (d) mid - range for the data and then (e) answer the given questions. listed below are the highest amounts of net worth (in millions of dollars) of all celebrities. what can be inferred about their precision? what do the results tell us about the population of all celebrities? based on the nature of the amounts, what can be inferred about their precision? 245 200 185 170 165 165 160 160 160 160

a. find the mean the mean is $177 million (type an integer or a decimal rounded to one decimal place as needed.)
b. find the median the median is $165 million (type an integer or a decimal rounded to one decimal place as needed.)

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points.
We have $x = [245,200,185,170,165,165,160,160,160,160]$, and $n = 10$.
$\sum_{i=1}^{10}x_{i}=245 + 200+185+170+165+165+160+160+160+160=1770$.
$\bar{x}=\frac{1770}{10}=177$.

Step2: Calculate the median

First, we order the data set: $[160,160,160,160,165,165,170,185,200,245]$.
Since $n = 10$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points.
The $\frac{n}{2}=5$th value is $165$ and the $(\frac{n}{2}+1) = 6$th value is $165$.
Median$=\frac{165 + 165}{2}=165$.

Step3: Calculate the mode

The mode is the data - point that appears most frequently in the data set.
In the data set $[160,160,160,160,165,165,170,185,200,245]$, the number $160$ appears $4$ times, more frequently than any other number. So the mode is $160$.

Step4: Calculate the mid - range

The mid - range is calculated as $\frac{\text{Maximum value}+\text{Minimum value}}{2}$.
The maximum value is $245$ and the minimum value is $160$.
Mid - range$=\frac{245 + 160}{2}=\frac{405}{2}=202.5$.

Answer:

a. $177$
b. $165$
c. $160$
d. $202.5$