the number of passenger electric vehicles registered is collected for the 39 counties of washington state…

the number of passenger electric vehicles registered is collected for the 39 counties of washington state. mean: 3,589.3 cars minimum: 3 cars q1: 170 cars median: 506 cars q3: 1,560 cars maximum: 73,996 cars 16,223 337 460 60 467 73,996 8,368 1,556 222 806 1,736 3 238 3,444 165 706 3,497 10,657 37 278 186 424 170 45 4,425 4,601 36 677 554 25 858 12 796 773 1,560 44 841 506 a. are any of the values outliers? explain or show your reasoning. b. if there are any outliers, why do you think they might exist? should they be included in an analysis of the data?

the number of passenger electric vehicles registered is collected for the 39 counties of washington state. mean: 3,589.3 cars minimum: 3 cars q1: 170 cars median: 506 cars q3: 1,560 cars maximum: 73,996 cars 16,223 337 460 60 467 73,996 8,368 1,556 222 806 1,736 3 238 3,444 165 706 3,497 10,657 37 278 186 424 170 45 4,425 4,601 36 677 554 25 858 12 796 773 1,560 44 841 506 a. are any of the values outliers? explain or show your reasoning. b. if there are any outliers, why do you think they might exist? should they be included in an analysis of the data?

Answer

Explanation:

Step1: Calculate the inter - quartile range (IQR).

$IQR = Q3 - Q1$ $IQR=1560 - 170=1390$

Step2: Calculate the lower fence.

Lower fence $=Q1-1.5\times IQR$ $=170-1.5\times1390=170 - 2085=-1915$

Step3: Calculate the upper fence.

Upper fence $=Q3 + 1.5\times IQR$ $=1560+1.5\times1390=1560 + 2085=3645$

Step4: Identify outliers.

Values less than the lower fence or greater than the upper fence are outliers. The values $16223$, $10657$, $4425$, $4601$, $73996$, $8368$ are greater than $3645$. So there are outliers.

Answer:

a. Yes, there are outliers. The outliers are values such as $16223$, $10657$, $4425$, $4601$, $73996$, $8368$ since they are greater than the upper - fence of $3645$. b. Outliers might exist because some counties could have a much larger population, more urban development, or more aggressive electric - vehicle promotion policies compared to other counties. Whether to include them in the data analysis depends on the purpose of the analysis. If the goal is to understand the typical situation of most counties, outliers may distort the results and could be removed. However, if the analysis aims to understand the full range of electric - vehicle adoption across all counties, including the most extreme cases, they should be included.