Question

find the (a) mean, (b) median, (c) mode, and (d) midrange 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 do the results tell us about the population of all celebrities? based on the amounts, what can be inferred about their precision? 245 200 185 170 165 165 160 160 160 160 a. apart from the fact that all other celebrities have amounts of net worth lower than those given, the results in parts (a), (b), and (d) do not given meaningful results. however, the result from part (c) shows that the most common celebrity net worth is equal to the mode. b. the results tell us that the most common celebrity net worth is the mode, but all other celebrities are expected to have net worths approximately equal to the median, or midrange. c. the results tell us that all celebrities are expected to have amounts of net worth approximately equal to one of the measures of center found in parts (a) through (d). d. apart from the fact that all other celebrities have amounts of net worth lower than those given, nothing meaningful can be known about the population. based on the nature of the amounts, what can be inferred about their precision? a. the values are all whole numbers, so they appear to be accurate to the nearest whole number. b. since no information is given, nothing can be said about the precision of the given values. c. since celebrity information is public, these values can be assumed to be unrounded. d. the values all end in 0 or 5, so they appear to be rounded estimates.

Explanation:

Step1: Calculate the mean

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. Here, $n = 10$, and $\sum_{i=1}^{10}x_{i}=245 + 200+185 + 170+165+165+160+160+160+160=1730$. So, $\bar{x}=\frac{1730}{10}=173$.

Step2: Calculate the median

First, order the data: $160,160,160,160,165,165,170,185,200,245$. Since $n = 10$ (an even number), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}=\frac{165 + 165}{2}=165$.

Step3: Calculate the mode

The mode is the most frequently occurring value. Here, the mode is $160$ as it appears $4$ times.

Step4: Calculate the mid - range

The mid - range $MR=\frac{\text{Max}+\text{Min}}{2}=\frac{245 + 160}{2}=\frac{405}{2}=202.5$.

Step5: Answer the first multiple - choice question

The sample size is small and may not be representative of the entire population of celebrities. Apart from the fact that all other celebrities have amounts of net worth lower than those given, nothing meaningful can be known about the population. So the answer to the first question is D.

Step6: Answer the second multiple - choice question

The values all end in 0 or 5, so they appear to be rounded estimates. So the answer to the second question is D.

Answer:

For the first multiple - choice question: D. Apart from the fact that all other celebrities have amounts of net worth lower than those given, nothing meaningful can be known about the population.
For the second multiple - choice question: D. The values all end in 0 or 5, so they appear to be rounded estimates.