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 amounts mean? what can be inferred about their precision? 245 200 185 170 165 165 160 160 160 160. b. there is no mode. d. find the midrange. the midrange is $202.5 million (type an integer or a decimal rounded to one decimal place as needed.) e. what do the results tell us about the population of all celebrities? 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 mean, 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.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $x_1 = 245,x_2=200,x_3 = 185,x_4=170,x_5=165,x_6=165,x_7=160,x_8=160,x_9=160,x_{10}=160$. $n = 10$. $\sum_{i=1}^{10}x_{i}=245 + 200+185+170+165+165+160+160+160+160=1760$. So, $\bar{x}=\frac{1760}{10}=176$.

Step2: Calculate the median

First, order the data: $160,160,160,160,165,165,170,185,200,245$. Since $n = 10$ (even), 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 value $160$ occurs $4$ times, so the mode is $160$.

Step4: Analyze part (e)

The data is a small sample of the highest - net - worth celebrities. The sample is not representative of all celebrities. Just because these are the highest amounts, we cannot make broad statements about all 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.

Answer:

a. Mean: $176$ million
b. Median: $165$ million
c. Mode: $160$ million
d. Mid - range: $202.5$ million
e. 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.