Question

the dataset 3, 6, 2, 8, 6, 6, 9, 10, 3 represents the scores on the most recent quiz. describe the change in the distribution of data if an additional number is added. if you add the score of 4, what part of the five - number summary will change? (1 point) o q3 o median o q1 o minimum

Explanation:

Step1: Sort the original dataset

Original dataset: \(2,3,3,6,6,6,8,9,10\)

Step2: Find the five - number summary of the original dataset

• Minimum: \(2\)
• \(Q1\): The median of the lower half. Lower half: \(2,3,3,6\). Median of lower half \(\frac{3 + 3}{2}=3\)
• Median: The middle value. Since \(n = 9\), the median is the 5th value, which is \(6\)
• \(Q3\): The median of the upper half. Upper half: \(6,8,9,10\). Median of upper half \(\frac{8+9}{2} = 8.5\)
• Maximum: \(10\)

Step3: Add the new number \(4\) and sort the new dataset

New dataset: \(2,3,3,4,6,6,6,8,9,10\)

Step4: Find the five - number summary of the new dataset

• Minimum: \(2\) (remains the same)
• \(Q1\): The median of the lower half. Lower half: \(2,3,3,4\). Median of lower half \(\frac{3+3}{2}=3\) (remains the same)
• Median: Since \(n = 10\), the median is \(\frac{6 + 6}{2}=6\) (remains the same)
• \(Q3\): The median of the upper half. Upper half: \(6,8,9,10\). Median of upper half \(\frac{8 + 9}{2}=8.5\) (remains the same)

Answer:

None of the five - number summary (minimum, \(Q1\), median, \(Q3\)) changes.