Find the five-number summary and the IQR. Min Q1 Median Q3 Max IQR (b) Calculate x and s (!!Round your standard deviation to three decimal places!!), and the z-score for the smallest and largest observations(!!Round your answers to two decimal places.!!) Consider the following data set: 7, 7, 1, 3, 7, 7, 4, 6, 6, 6, 3, 0. (a) Find the five-number summary and the IQR. Min Q1 Median Q3 Max IQR (b) Calculate x and s (!!Round your standard deviation to three decimal places!!), and the z-score for the smallest and largest observations(!!Round your answers to two decimal places.!!) z-score for smaller observation z = z-score for larger observation z = Is either of these observations unusually large or unusually small? A. Since neither z-score exceeds 2 in absolute value, none of the observations are unusually small or large. B. Since the z-score for the larger observation is larger than 2 in absolute value, the larger value is unusually large. C. Since both z-scores exceed 2 in absolute value, both of the observations are unusual. D. Since the z-score for the smaller observation is larger than 2 in absolute value, the smaller value is unusually small.
The Correct Answer and Explanation is :
(a) Five-number summary and IQR:
- Min: 0
- Q1: 3.0
- Median: 6.0
- Q3: 7.0
- Max: 7
- IQR (Interquartile Range): 4.0
(b) Calculations for mean, standard deviation, and z-scores:
- Mean (x): 4.75
- Standard deviation (s): 2.491
- Z-score for the smallest observation (0): -1.91
- Z-score for the largest observation (7): 0.9
Answer for unusual observations:
Given the z-scores of the smallest and largest observations:
- The z-score for the smallest observation is -1.91, and the z-score for the largest observation is 0.9. Neither of these z-scores exceeds an absolute value of 2.
Thus, the correct answer is A: Since neither z-score exceeds 2 in absolute value, none of the observations are unusually small or large.
Now, I will generate a visualization to help illustrate these values.
Here is a box plot visualizing the five-number summary and the IQR of your data set. The plot clearly shows the minimum, Q1, median, Q3, and maximum values, with the IQR represented by the width of the box.
Let me know if you need further explanation or if you’d like another visualization!
