Question

a college student would like to investigate the prices of sandwiches offered near the campus. a sample of 50 shops that sell sandwiches near the campus was taken and the price they charge for a large sandwich was recorded. the results are displayed in the cumulative relative frequency histogram below. which interval contains the median sandwich price? $9 - $10 $10 - $11 $11 - $12 $12 - $13 large sandwich prices

Explanation:

Step1: Understand the median

The median of a data set with \(n = 50\) values is the \(\frac{n + 1}{2}=\frac{50+1}{2}=25.5^{th}\) value. In terms of cumulative relative frequency, we look for the interval where the cumulative relative frequency first exceeds \(50\%\) (since \(25.5\) out of \(50\) is \(51\%\)).

Step2: Analyze the cumulative relative - frequency histogram

Cumulative relative frequency represents the proportion of data values that are less than or equal to the upper - bound of an interval.

• For the \(\$9 - \$10\) interval: Suppose the cumulative relative frequency is less than \(50\%\) (from the shape of the histogram, if we assume the first non - zero bar is for \(\$9 - \$10\) and it does not reach \(50\%\)).
• For the \(\$10 - \$11\) interval: The cumulative relative frequency will cross the \(50\%\) mark.

Answer:

\(\$10 - \$11\)