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, 2009. 5, 9, 2008. 5, 8, 7, 7. 5, 6, 2006. 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 1

Please find attached the drawing of the histogram of the given data

created with MS Excel.

The statement that is true about the histogram is the option;  

• A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.

Reasons:

The given data sorted in increasing order are presented as follows;

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

From the data given above, we have;

The number of data points, n = 15

The median, Q₂ = (n + 1)÷ 2th data point = The 8th term = 7.5

The mean = 7.433

• The information displayed on a histogram is the way a continuous data is shaped and the way the data is spread.

The data points in 1 minute increments are presented as follows;

5.5 to 6.5 = 5 data points

6.5 to 7.5 = 4 data points

7.5 to 8.5 = 3 data points

8.5 to 9.5 = 2 data points

9.5 to 10.5 = 1 data point

Therefore, most of the data are between 5.5 to 8.5, with one-third of the data being within the class 5.5 to 6.5 range.

Therefore, the histogram is right skewed.

The median is given by the value at which the graph is shared into equal halves.

• The median = 7.5

The mean is given by the sum of the values divided by the number of values.

• The mean = 7.433

Therefore, the statement that is true about the histogram is; A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.

Learn more about histograms here:

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