Asked by Madison
11, 12, 32, 43, 45, 48, 48, 48
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GPT-5 mini
AI
Here are some common descriptive statistics for the data set {11, 12, 32, 43, 45, 48, 48, 48} (n = 8):
- Sorted data: 11, 12, 32, 43, 45, 48, 48, 48
- Count (n): 8
- Sum: 287
- Mean (average): 35.875
- Median: 44 (average of 4th and 5th values: (43+45)/2)
- Mode: 48 (occurs 3 times)
- Range: 48 − 11 = 37
- First quartile (Q1): 22 (median of 11,12,32,43)
- Third quartile (Q3): 48 (median of 45,48,48,48)
- Interquartile range (IQR): Q3 − Q1 = 26
Variance and standard deviation:
- Sum of squared deviations from the mean = 1778.875
- Population variance (σ^2) = 1778.875 / 8 = 222.359375
- Population standard deviation (σ) ≈ 14.911
- Sample variance (s^2) = 1778.875 / (8−1) = 254.125
- Sample standard deviation (s) ≈ 15.941
Would you like a boxplot, histogram, or any other analysis (e.g., mean absolute deviation or confidence interval)?
- Sorted data: 11, 12, 32, 43, 45, 48, 48, 48
- Count (n): 8
- Sum: 287
- Mean (average): 35.875
- Median: 44 (average of 4th and 5th values: (43+45)/2)
- Mode: 48 (occurs 3 times)
- Range: 48 − 11 = 37
- First quartile (Q1): 22 (median of 11,12,32,43)
- Third quartile (Q3): 48 (median of 45,48,48,48)
- Interquartile range (IQR): Q3 − Q1 = 26
Variance and standard deviation:
- Sum of squared deviations from the mean = 1778.875
- Population variance (σ^2) = 1778.875 / 8 = 222.359375
- Population standard deviation (σ) ≈ 14.911
- Sample variance (s^2) = 1778.875 / (8−1) = 254.125
- Sample standard deviation (s) ≈ 15.941
Would you like a boxplot, histogram, or any other analysis (e.g., mean absolute deviation or confidence interval)?
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