students in a fitness class each completed a one - mile walk or run. the list shows the time it took each…

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.

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.

Answer

Explanation:

Step1: Analyze data distribution

First, list - count the data values: 5.5 appears 3 times, 6 appears 3 times, 6.5 appears 1 time, 7 appears 2 times, 7.5 appears 3 times, 8 appears 3 times, 8.5 appears 2 times, 9 appears 2 times, 9.5 appears 1 time, 10 appears 1 time.

Step2: Evaluate mean - median relationship

To find the median, 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, 8.5, 9, 9, 9.5, 10. There are 20 data points. The median is the average of the 10th and 11th values, which is $\frac{7.5 + 7.5}{2}=7.5$. To estimate the mean, $\sum x = 5.5\times3+6\times3 + 6.5\times1+7\times2+7.5\times3+8\times3+8.5\times2+9\times2+9.5\times1+10\times1=153.5$, and the mean $\bar{x}=\frac{153.5}{20}=7.675$. The mean is greater than the median.

Step3: Analyze shape of histogram

The data has most of the values clustered between 6 and 9 minutes. The distribution is not symmetric (not normal - curve - shaped) and is not left - skewed.

Answer:

The histogram will show that the mean time is greater than the median time of 7.5 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.