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)

Question

Responses

minimum
minimum

median
median

Q3
Q3

Q1

Answer 1

To analyze how the addition of the score of 4 will affect the five-number summary of the dataset, we first need to find the current five-number summary of the original dataset: 3, 6, 2, 8, 6, 6, 9, 10, 3.

1. Ordering the dataset:

   • Ordered data: 2, 3, 3, 6, 6, 6, 8, 9, 10

2. Finding the five-number summary:

   • Minimum: 2
   • Q1 (first quartile): The median of the first half (2, 3, 3, 6) is 3.
   • Median: The median of the dataset (6) is the middle value in the ordered list.
   • Q3 (third quartile): The median of the second half (6, 6, 8, 9, 10) is 8.
   • Maximum: 10

So the five-number summary before adding the score of 4 is:

• Minimum: 2
• Q1: 3
• Median: 6
• Q3: 8
• Maximum: 10

3. Adding the score of 4:

   • New dataset: 2, 3, 3, 4, 6, 6, 6, 8, 9, 10

4. Re-ordering the new dataset:

   • Ordered data: 2, 3, 3, 4, 6, 6, 6, 8, 9, 10

5. Re-evaluating the five-number summary:

   • Minimum: 2 (remains the same)
   • Q1: The new first half is (2, 3, 3, 4, 6) - Q1 is 3 (remains the same)
   • Median: The new median of the even dataset (6, 6) is (6 + 6)/2 = 6 (remains the same)
   • Q3: The new second half is (6, 6, 8, 9, 10) - Q3 now takes the average of 8 and 9, which is (8 + 9)/2 = 8.5 (changes from 8 to 8.5)
   • Maximum: 10 (remains the same)

Given this analysis, the only part of the five-number summary that changes when adding the score of 4 is Q3.

Thus, the correct response is: Q3