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: Arrange data in ascending order

$5.5,5.5,5.5,6,6,6,6.5,7,7,7.5,7.5,7.5,8,8,8,8.5,9,9,9.5,10$

Step2: Calculate the median

There are $n = 20$ data - points. The median is the average of the 10th and 11th ordered values. $\text{Median}=\frac{7.5 + 7.5}{2}=7.5$

Step3: Calculate the mean

$\text{Mean}=\frac{5.5\times3+6\times3 + 6.5\times1+7\times2+7.5\times3+8\times3+8.5\times1+9\times2+9.5\times1+10\times1}{20}=\frac{16.5 + 18+6.5 + 14+22.5+24+8.5+18+9.5+10}{20}=\frac{148}{20}=7.4$

Step4: Analyze the shape of the data

Most of the data values are in the range of $6 - 9$ minutes. The data has a single - peak and is somewhat symmetric. It can be approximated by a normal curve.

Answer:

A. A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.
D. The shape of the histogram can be approximated with a normal curve.
E. The histogram will show that most of the data is centered between 6 minutes and 9 minutes.