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What percentage of the data values falls between the values of 3 and 24 in the data set shown? A box-and-whisker plot. The numb...Question
What percentage of the data values falls between the values of 27 and 45 in the data set shown?
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
25%
50%
75%
100%
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
25%
50%
75%
100%
Answers
GPT-4o mini
To determine the percentage of data values that fall between the values of 27 and 45 based on the provided box-and-whisker plot information, let's break down the components:
- The lower whisker (27) represents the minimum value (smallest data point).
- The lower edge of the box (32) represents the first quartile (Q1), which is the 25th percentile.
- The line inside the box (36) represents the median (Q2), which is the 50th percentile.
- The upper edge of the box (45) represents the third quartile (Q3), which is the 75th percentile.
- The upper whisker (48) represents the maximum value (largest data point).
From this information, we can determine the distribution of the data:
- The range from 27 to 45 covers:
- All data from the minimum (27) to the upper edge of the box (45).
- The values below 27 are not included.
- The values above 45 (specifically from 45 to 48) fall within the upper whisker but do not impact the count for the range we are focusing on.
Since the lower quartile (Q1, 32) to the upper quartile (Q3, 45) represents 50% of the data (from Q1 to Q3 encompasses values from the 25th percentile to the 75th percentile), and since the data from the minimum (27) to Q1 (32) also includes values leading up to the lower quartile, we can assess this simply:
- 100% of the values from 27 (minimum) to the third quartile (Q3 at 45) includes both:
- 25% of the data from 27 to 32
- 50% of the data from 32 to 45
Adding these percentages together gives:
- From 27 to 32: 25%
- From 32 to 45: 50%
Adding these together gives:
**25% + 50% = 75%**
Thus, **the percentage of the data values that fall between 27 and 45 is 75%**.
The correct answer is **75%.**
- The lower whisker (27) represents the minimum value (smallest data point).
- The lower edge of the box (32) represents the first quartile (Q1), which is the 25th percentile.
- The line inside the box (36) represents the median (Q2), which is the 50th percentile.
- The upper edge of the box (45) represents the third quartile (Q3), which is the 75th percentile.
- The upper whisker (48) represents the maximum value (largest data point).
From this information, we can determine the distribution of the data:
- The range from 27 to 45 covers:
- All data from the minimum (27) to the upper edge of the box (45).
- The values below 27 are not included.
- The values above 45 (specifically from 45 to 48) fall within the upper whisker but do not impact the count for the range we are focusing on.
Since the lower quartile (Q1, 32) to the upper quartile (Q3, 45) represents 50% of the data (from Q1 to Q3 encompasses values from the 25th percentile to the 75th percentile), and since the data from the minimum (27) to Q1 (32) also includes values leading up to the lower quartile, we can assess this simply:
- 100% of the values from 27 (minimum) to the third quartile (Q3 at 45) includes both:
- 25% of the data from 27 to 32
- 50% of the data from 32 to 45
Adding these percentages together gives:
- From 27 to 32: 25%
- From 32 to 45: 50%
Adding these together gives:
**25% + 50% = 75%**
Thus, **the percentage of the data values that fall between 27 and 45 is 75%**.
The correct answer is **75%.**