Question

here are 6 celebrities with some of the highest net worths (in millions of dollars) in a recent year: oprah winfrey (3200), michael jordan (1700), paul mccartney (1200), j. k. rowling (1000), david copperfield (1000), and jerry seinfeld (950). find the range, variance, and standard deviation for the sample data. 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? the range is $ million. (round to the nearest integer as needed)

Explanation:

Step1: Find the range

The range is the difference between the maximum and minimum values. The maximum value is 3200 and the minimum value is 950.
$3200 - 950=2250$

Step2: Calculate the mean

The data set is $x = \{3200,1700,1200,1000,1000,950\}$. The mean $\bar{x}=\frac{3200 + 1700+1200+1000+1000+950}{6}=\frac{9050}{6}\approx1508.33$

Step3: Calculate the squared - differences

$(3200 - 1508.33)^2=(1691.67)^2 = 2861718.7889$, $(1700 - 1508.33)^2=(191.67)^2=36737.1889$, $(1200 - 1508.33)^2=(- 308.33)^2 = 95067.9889$, $(1000 - 1508.33)^2=(-508.33)^2 = 258499.3889$, $(1000 - 1508.33)^2=(-508.33)^2 = 258499.3889$, $(950 - 1508.33)^2=(-558.33)^2 = 311733.3889$

Step4: Calculate the variance

The variance $s^{2}=\frac{2861718.7889+36737.1889+95067.9889+258499.3889+258499.3889+311733.3889}{6 - 1}=\frac{3822255.1334}{5}=764451.0267$

Step5: Calculate the standard deviation

The standard deviation $s=\sqrt{764451.0267}\approx874.22$

The results for the sample data: The range of the net - worths of these 6 celebrities is a large value, indicating a wide spread between the highest and lowest net - worths in the sample. The variance and standard deviation also suggest that there is a significant amount of variation in the net - worths of these celebrities. However, since this is just a sample of 6 celebrities, it may not be fully representative of the entire population of all celebrities. Regarding precision, the net - worths are given as whole numbers in millions of dollars, so the precision is to the nearest million dollars.

Answer:

The range is $2250$ million. The variance is approximately $764451.03$ (in millions of dollars squared) and the standard deviation is approximately $874.22$ million. The large range, variance and standard deviation of the sample indicate a wide spread in net - worths among the sampled celebrities. Since it's a small sample, it may not represent the whole population well. The precision of the amounts is to the nearest million dollars.