Question

HH.1 Calculate mean, median, mode, and range
U2A
A music student is cataloging some songs and noting the length of each. The 7 songs have lengths of:
1 minute1 minute4 minutes3 minutes6 minutes6 minutes7 minutes
What is the mean song length?

minutes

Answer 1

To calculate the mean song length, we need to sum the lengths of the songs and then divide by the number of songs.

The lengths of the songs are:
1 minute, 1 minute, 4 minutes, 3 minutes, 6 minutes, 6 minutes, and 7 minutes.

1. **Calculate the total sum of the lengths**:

\[
1 + 1 + 4 + 3 + 6 + 6 + 7 = 28 \text{ minutes}
\]

2. **Count the number of songs**:

There are 7 songs.

3. **Calculate the mean**:

\[
\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Songs}} = \frac{28}{7} = 4 \text{ minutes}
\]

Thus, the mean song length is **4 minutes**.

Now, let's also calculate the median, mode, and range:

4. **Median**:
- To find the median, we need to sort the song lengths in ascending order:
- Sorted lengths: 1, 1, 3, 4, 6, 6, 7.
- The median is the middle value. Since there are 7 values (an odd number), the median is the 4th value:
\[
\text{Median} = 4 \text{ minutes}
\]

5. **Mode**:
- The mode is the number that appears most frequently. In the sorted list (1, 1, 3, 4, 6, 6, 7), both 1 and 6 appear twice.
\[
\text{Mode} = 1 \text{ and } 6 \text{ minutes}
\]

6. **Range**:
- The range is the difference between the longest and shortest songs:
\[
\text{Range} = \text{Longest} - \text{Shortest} = 7 - 1 = 6 \text{ minutes}
\]

In summary:
- **Mean**: 4 minutes
- **Median**: 4 minutes
- **Mode**: 1 and 6 minutes
- **Range**: 6 minutes