Question

students in a fitness class each completed a one - mile walk or run. the list shows the time it took each person to complete the mile. each time is rounded to the nearest half - minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
which statements are true about a histogram with one - minute increments representing the data? select three options.
□ a histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.
□ the histogram will have a shape that is left - skewed.
□ the histogram will show that the mean time is greater than the median time of 7.4 minutes.
□ the shape of the histogram can be approximated with a normal curve.
□ the histogram will show that most of the data is centered between 6 minutes and 9 minutes.

Explanation:

Step1: Sort the data

Sort the data in ascending order: \(5.5,5.5,6,6,6.5,7,7,7.5,7.5,8,8,8,8.5,9,9.5,10\)

Step2: Calculate the median

Since there are \(n = 16\) data points, the median is the average of the \(8^{th}\) and \(9^{th}\) values. The \(8^{th}\) value is \(7.5\) and the \(9^{th}\) value is \(8\). Median \(M=\frac{7.5 + 8}{2}=7.75\)

Step3: Calculate the mean

Mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{5.5\times2+6\times2 + 6.5+7\times2+7.5\times2+8\times3+8.5+9\times2+9.5+10}{16}=\frac{11 + 12+6.5 + 14+15+24+8.5+18+9.5+10}{16}=\frac{128.5}{16}\approx8.03\)

Step4: Analyze the shape

Since the mean (\(\approx8.03\)) is greater than the median (\(7.75\)), the data is right - skewed. But most of the data (13 out of 16) lies between \(6\) and \(9\) minutes. A normal curve can approximate the shape of the histogram (even though it is slightly skewed, the general mound - like shape is present)

Answer:

The histogram will show that the mean time is greater than the median time of \(7.4\) minutes. The shape of the histogram can be approximated with a normal curve. The histogram will show that most of the data is centered between \(6\) minutes and \(9\) minutes.