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 50


Calculate the mean, median, range, and midrange of the train ride times for the week.

Answer 1

To calculate the mean, median, range, and midrange of Santos's train ride times, we will start by organizing the data he collected:

- Train ride times in minutes: 48, 51, 48, 50

### 1. Mean
The mean is calculated by adding all the values together and then dividing by the number of values.

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{48 + 51 + 48 + 50}{4}
\]
\[
\text{Mean} = \frac{197}{4} = 49.25
\]

### 2. Median
To find the median, we first need to arrange the data in ascending order:

- Ordered data: 48, 48, 50, 51

Since there is an even number of values (4), the median will be the average of the two middle numbers.

\[
\text{Median} = \frac{48 + 50}{2} = \frac{98}{2} = 49
\]

### 3. Range
The range is found by subtracting the smallest value from the largest value.

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

### 4. Midrange
The midrange is calculated by averaging the maximum and minimum values.

\[
\text{Midrange} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{51 + 48}{2} = \frac{99}{2} = 49.5
\]

### Summary
- Mean: 49.25
- Median: 49
- Range: 3
- Midrange: 49.5

Thus, the statistical measures are as follows:

- **Mean**: 49.25
- **Median**: 49
- **Range**: 3
- **Midrange**: 49.5