14. One weekend a salesperson sold cars for $$ \$ 22,000 ; \$ 20,000 ; \$ 8000 ; \$ 22,000 $$; and $$ \$ 24,000 $$. What is the outlier in this set of data? What effect does the outlier have when interpreting the mean price of the cars sold?

Question

UpStudy AI · Accepted Answer

1. List the car prices as given:  
   $$
   22\,000, \quad 20\,000, \quad 8\,000, \quad 22\,000, \quad 24\,000.
   $$

2. Notice that most prices are clustered between $$20\,000$$ and $$24\,000$$ dollars, with the exception of $$\boxed{8\,000}$$ dollars. This value is significantly lower than the others, making it the outlier.

3. To see the effect of the outlier on the mean, first calculate the mean of the data set.

4. Compute the sum of all the car prices:
   $$
   22\,000 + 20\,000 + 8\,000 + 22\,000 + 24\,000 = 96\,000.
   $$

5. Since there are 5 data points, the mean is given by:
   $$
   \text{Mean} = \frac{96\,000}{5} = 19\,200.
   $$

6. Notice that without the outlier $$8\,000$$, the remaining data values would be:
   $$
   22\,000, \quad 20\,000, \quad 22\,000, \quad 24\,000.
   $$
   Their sum would be:
   $$
   22\,000 + 20\,000 + 22\,000 + 24\,000 = 88\,000.
   $$
   And the mean for these 4 values would be:
   $$
   \frac{88\,000}{4} = 22\,000.
   $$

7. The outlier $$8\,000$$ decreases the mean from $$22\,000$$ to $$19\,200$$. This lower mean value does not properly represent the typical sales price for the majority of the cars sold.

8. Conclusion:  
   - The outlier is $$\boxed{\$8\,000}$$.  
   - Its presence lowers the mean, making it less representative of the central tendency of the data since most prices are significantly higher.
The outlier is \$8,000. Its presence lowers the mean price, making it less representative of the typical sales price for the majority of the cars sold.

14. One weekend a salesperson sold cars for \( \$ 22,000 ; \$ 20,000 ; \$ 8000 ; \$ 22,000 \); and \( \$ 24,000 \). What is the outlier in this set of data? What effect does the outlier have when interpreting the mean price of the cars sold?

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Statistics Questions