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.
- Calculate the total sum of the lengths:
\[ 1 + 1 + 4 + 3 + 6 + 6 + 7 = 28 \text{ minutes} \]
- Count the number of songs:
There are 7 songs.
- 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:
-
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: \[ \text{Median} = 4 \text{ minutes} \]
-
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. \[ \text{Mode} = 1 \text{ and } 6 \text{ minutes} \]
-
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