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: Ordenar los datos

Ordenamos los datos: 5.5, 5.5, 6, 6, 6.5, 7, 7, 7.5, 7.5, 8, 8, 8.5, 8.5, 9, 9.5, 10.

Step2: Calcular la mediana

Como hay 16 datos, la mediana es el promedio del 8º y 9º valor ordenados. $(7.5 + 7.5)/2=7.5$.

Step3: Analizar la forma de la distribución

Al observar los datos, vemos que la mayoría está entre 6 y 9 minutos, lo que sugiere que la forma se puede aproximar a una curva normal y que el promedio y la mediana serán cercanos. La forma no es asimétrica hacia la izquierda.

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.