Question

question 6 of 17 > suppose that the weekly unit sales for two small franchise stores in texas and new york are recorded over a one - year period. the following boxplots display the resulting weekly unit sales in intervals of 25. select all of the statements that describe the two boxplots above. the first quartile of weekly unit sales in texas is less than the first quartile of weekly unit sales in new york. weekly unit sales in texas are more consistent than weekly sales in new york. the top 25% of weekly unit sales in new york has less variation than the top 25% of weekly sales in texas. the median of weekly unit sales in texas is greater than the median of weekly sales in new york. weekly unit sales in new york have more extreme values than weekly sales in texas.

Explanation:

Step1: Analyze first - quartile

In a box - plot, the left - hand side of the box represents the first quartile ($Q_1$). Looking at the box - plots, the first quartile of Texas sales is around 175 and for New York it is around 150. So the statement "The first quartile of weekly unit sales in Texas is less than the first quartile of weekly unit sales in New York" is false.

Step2: Analyze consistency (inter - quartile range)

Consistency is related to the inter - quartile range (IQR = $Q_3 - Q_1$). A smaller IQR means more consistency. The IQR for Texas appears to be smaller than that for New York, so weekly unit sales in Texas are more consistent. This statement is true.

Step3: Analyze top 25% variation

The top 25% of the data is from $Q_3$ to the maximum value. The length of the right - hand whisker and the part of the box from $Q_3$ to the maximum for New York is shorter than that for Texas, so the top 25% of weekly unit sales in New York has less variation. This statement is true.

Step4: Analyze median

The line inside the box represents the median. The median of Texas sales is around 200 and the median of New York sales is around 200 as well. So the statement "The median of weekly unit sales in Texas is greater than the median of weekly sales in New York" is false.

Step5: Analyze extreme values

Extreme values are represented by the whiskers. The whiskers for New York are longer than those for Texas, so weekly unit sales in New York have more extreme values. This statement is true.

Answer:

• Weekly unit sales in Texas are more consistent than weekly sales in New York.
• The top 25% of weekly unit sales in New York has less variation than the top 25% of weekly sales in Texas.
• Weekly unit sales in New York have more extreme values than weekly sales in Texas.