To summarize the data set 20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32, let's calculate the measures of center: mean, median, and mode.
Data set: 20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32.
1. Mean
Mean = (Sum of all values) / (Number of values)
Sum = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 +
Sum = (20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32) = 16 + 13 + 20 + 20 + 15 + 18 + 21 + 30 + 28 + 32 + 20 + 32 + 32 + 32 + 32 = 453
Count = 15
Mean = 453 / 15 = 30.2
2. Median
To find the median, we first arrange the data in ascending order:
Sorted Data: 13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
Since there are 15 numbers (an odd count), the median is the middle number (8th number):
Median = 21
3. Mode
The mode is the number that appears most frequently:
20 appears 3 times, 32 appears 4 times.
Mode = 32
Conclusion
- Mean: 30.2
- Median: 21
- Mode: 32
Correct Option
Looking for the option that matches these results, none of the given options (A, B, C, D) were correct based on this calculation. Please check the values again if any errors occurred in transcribing the dataset.