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 $ 2250 million. (round to the nearest integer as needed.) the variance is \\(\square\\) million dollars squared. (round to the nearest integer as needed.)

Explanation:

Step1: Identify the data set

The net worths (in millions of dollars) are: 3200, 1700, 1200, 1000, 1000, 950.

Step2: Calculate the mean ($\bar{x}$)

First, find the sum of the data: $3200 + 1700 + 1200 + 1000 + 1000 + 950 = 9050$.
There are 6 data points, so the mean is $\bar{x} = \frac{9050}{6} \approx 1508.3333$.

Step3: Calculate the squared differences from the mean

For each data point $x_i$, calculate $(x_i - \bar{x})^2$:

• $(3200 - 1508.3333)^2 \approx (1691.6667)^2 \approx 2861736.111$
• $(1700 - 1508.3333)^2 \approx (191.6667)^2 \approx 36736.111$
• $(1200 - 1508.3333)^2 \approx (-308.3333)^2 \approx 95070.833$
• $(1000 - 1508.3333)^2 \approx (-508.3333)^2 \approx 258390.278$
• $(1000 - 1508.3333)^2 \approx (-508.3333)^2 \approx 258390.278$
• $(950 - 1508.3333)^2 \approx (-558.3333)^2 \approx 311745.833$

Step4: Sum the squared differences

Sum these values: $2861736.111 + 36736.111 + 95070.833 + 258390.278 + 258390.278 + 311745.833 \approx 3822069.444$.

Step5: Calculate the sample variance

The sample variance ($s^2$) is the sum of squared differences divided by $n - 1$ (where $n = 6$), so $s^2 = \frac{3822069.444}{5} \approx 764413.8888$.

Step6: Round to the nearest integer

Rounding $764413.8888$ to the nearest integer gives 764414.

Answer:

764414