Last year, Greg got a new job managing the gift shop at the Bern Valley Zoo. One of his responsibilities was to track the shop's total sales each day. This box plot shows the results.

Gift shop sales ($)
200
250
300
350
400
450
What percent of the time did the gift shop have sales of $350 or less?
%

1 answer

To determine what percent of the time the gift shop had sales of $350 or less, we need to analyze the box plot. Here's how to interpret it:

  1. Identify the Quartiles: A box plot typically represents the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

  2. Locate Q1: Q1 marks the 25th percentile, meaning 25% of the data is below this value.

  3. Locate Q2 (the median): Q2 marks the 50th percentile, meaning 50% of the data is below this value.

  4. Locate Q3: Q3 marks the 75th percentile, meaning 75% of the data is below this value.

  5. Check where $350 falls: If $350 is equal to or below the median (Q2) of the sales data, then at least 50% of the sales were $350 or below. If $350 is between Q2 and Q3, then we need to consider if it falls within the IQR (interquartile range).

Assuming that based on the box plot:

  • If Q1 is less than $350 or Q2 is exactly $350, then we can conclude that 50% of the sales are below or equal to $350.
  • If $350 is less than Q3, and given that Q3 is the 75th percentile, then the percentage of days with sales of $350 or less would be equal to the percentage of days up to Q2 (50%) plus any sales between Q2 and $350.

Therefore, to achieve an accurate answer, we need to determine the exact position of $350 in relation to the quartiles displayed in the box plot.

Without the specific details of the quartiles, if we assume it aligns to the following common scenario, we could hypothesize:

  • If Q2 is $350, then 50% of the time the shop had sales of $350 or less.
  • If Q3 is over $350, it could be 50% + the additional percentage up to Q3.

Since we cannot see the box plot provided in your question, please apply this analysis to your specific case and provide necessary details if required for further assistance. Based on a straightforward interpretation, the answer is likely 50% if $350 corresponds with the median.