Given the dataset 68, 85, 88, 97, 85, 89, 98, 93, 95, and 99, what parts of the five-number summary would change if a new data point of 97 was added?(1 point)

Question

Responses

the median and Q3
the median and Q3

the minimum
the minimum

the maximum and the median
the maximum and the median

the median
the median

Answer 1

To determine what parts of the five-number summary would change when adding a new data point of 97 to the dataset, let's first find the current five-number summary (minimum, Q1, median, Q3, and maximum) of the original dataset:

Original dataset: 68, 85, 88, 97, 85, 89, 98, 93, 95, 99

1. Minimum: 68
2. Maximum: 99
3. Median: The dataset has 10 values. The median will be the average of the 5th and 6th values when arranged in ascending order:
   • Ordered dataset: 68, 85, 85, 88, 89, 93, 95, 97, 98, 99
   • Median = (89 + 93) / 2 = 91
4. Q1: The median of the lower half (68, 85, 85, 88, 89) is 85.
5. Q3: The median of the upper half (93, 95, 97, 98, 99) is 97.

Now, let's add the new data point of 97 to the dataset: New dataset: 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99

Recalculate the five-number summary:

1. Minimum: 68 (remains unchanged)
2. Maximum: 99 (remains unchanged)
3. Median: There are now 11 values. The median is the 6th value:
   • Ordered dataset: 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99
   • Median = 93 (now changes)
4. Q1: The median of the lower half (68, 85, 85, 88, 89) is 85 (remains unchanged).
5. Q3: The median of the upper half (95, 97, 97, 98, 99) is 97 (remains unchanged).

From this analysis, the affected components are the median (it changes from 91 to 93) and Q3 (it changes from 97 to 97, which remains unchanged).

Thus, the correct response is: the median and Q3.