Question

santos takes the train into the city five days a week for work. for one work week, he kept track of how many minutes long each train ride was:
48 51 48 48 50
calculate the mean, median, range, and midrange of the train ride times for the week.
mean, 49.5; median, 49; range, 48; midrange, 3
mean, 49; median, 48; range, 3; midrange, 49.5
mean, 48; median, 3; range, 49.5; midrange, 49
mean, 3; median, 49.5; range, 49; midrange, 48

Explanation:

Order the data set

To analyze the train ride times, we first arrange the five data points in ascending order:

$$ 48, 48, 48, 50, 51 $$

Calculate the mean

Using the Arithmetic Mean knowledge point

$$ \text{Mean} = \frac{48 + 51 + 48 + 48 + 50}{5} = \frac{245}{5} = 49 $$

Find the median

The median is the middle value of an ordered data set.
For our ordered set \(48, 48, 48, 50, 51\), the middle value (third value) is:

$$ \text{Median} = 48 $$

Calculate the range

The range is the difference between the maximum and minimum values in a data set.

$$ \text{Range} = \text{Maximum} - \text{Minimum} = 51 - 48 = 3 $$

Calculate the midrange

The midrange is the average of the maximum and minimum values in a data set.

$$ \text{Midrange} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{51 + 48}{2} = 49.5 $$

Answer:

• (A) Mean, 49.5; Median, 49; Range, 48; Midrange, 3
• (B) Mean, 49; Median, 48; Range, 3; Midrange, 49.5 (Correct answer)
• (C) Mean, 48; Median, 3; Range, 49.5; Midrange, 49
• (D) Mean, 3; Median, 49.5; Range, 49; Midrange, 48