Question

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box-and-whisker plots: a way of show the range of the data among the quartiles.

1. what is the median of each set:
2. which plot has a lesser range:
3. which plot has the greater interquartile range?
4. what is the upper quartile of each set?
5. what is the lower extreme of each set?
6. what percent of the data in plot b is between 60 and 85?
7. what percent of the data in plot a is greater than 80?
8. what percent of the data in plot b is less than 85?

Explanation:

Step1: Analyze Median (Plot A and B)

The median in a box - and - whisker plot is the line inside the box. For Plot A, the median line is at 65. For Plot B, the median line is at 70.

Step2: Analyze Range (Range = Max - Min)

For Plot A: Min is 45, Max is 100. Range = \(100 - 45=55\). For Plot B: Min is 40, Max is 100. Range = \(100 - 40 = 60\). So Plot A has a lesser range.

Step3: Analyze Interquartile Range (IQR=Q3 - Q1)

For Plot A: Q1 is 60, Q3 is 80. IQR=\(80 - 60 = 20\). For Plot B: Q1 is 60, Q3 is 85. IQR=\(85 - 60=25\). So Plot B has a greater IQR.

Step4: Analyze Upper Quartile (Q3)

Upper quartile is the right end of the box. For Plot A, Q3 = 80. For Plot B, Q3 = 85.

Step5: Analyze Lower Extreme (Min)

Lower extreme is the left - most dot (whisker start). For Plot A, lower extreme = 45. For Plot B, lower extreme = 40.

Step6: Percent of data in Plot B between 60 and 85

In a box - and - whisker plot, the data between Q1 and Q3 is 50%? No, wait. The interquartile range (Q3 - Q1) contains 50% of the data? No, actually, the data from Q1 to Q3 is 50%? Wait, no. The median divides the data into two halves (50% each). The interquartile range (Q1 to Q3) contains 50% of the data? Wait, no, the IQR contains 50% of the data? Wait, no, the data from the minimum to Q1 is 25%, Q1 to median is 25%, median to Q3 is 25%, Q3 to maximum is 25%. Wait, no, the correct breakdown is: the lower 25% of data is from min to Q1, the next 25% (25 - 50th percentile) is from Q1 to median, the next 25% (50 - 75th percentile) is from median to Q3, and the upper 25% is from Q3 to max. So for Plot B, Q1 = 60, Q3 = 85. So the data between 60 (Q1) and 85 (Q3) is from Q1 to Q3, which is 50% of the data? Wait, no, Q1 is the 25th percentile, Q3 is the 75th percentile. So the data between Q1 and Q3 is 75 - 25 = 50%? Wait, no, 75 - 25=50? Wait, 25th to 75th percentile is 50% of the data. So the data between 60 (Q1) and 85 (Q3) in Plot B is 50%? Wait, no, let's re - calculate. The percentage of data between Q1 and Q3 is 50%? Wait, no, the total data is 100%. The data below Q1: 25%, between Q1 and median:25%, between median and Q3:25%, above Q3:25%. So between Q1 and Q3, it's 25%+25% = 50%. So in Plot B, Q1 = 60, Q3 = 85. So the data between 60 and 85 is 50%? Wait, but let's check the values. Wait, maybe I made a mistake. Wait, the question is "What percent of the data in plot B is between 60 and 85?". Since 60 is Q1 (25th percentile) and 85 is Q3 (75th percentile), the percentage of data between 25th and 75th percentile is 75 - 25=50%? Wait, no, 75 - 25 = 50? Wait, 25th percentile to 75th percentile is 50% of the data. So the answer is 50%? Wait, no, wait. The interquartile range (IQR) is Q3 - Q1, and it contains 50% of the data. So yes, between Q1 (60) and Q3 (85) in Plot B, the percentage of data is 50%.

Step7: Percent of data in Plot A greater than 80

In Plot A, Q3 = 80. The data greater than Q3 is 25% (since Q3 is the 75th percentile, so 100 - 75 = 25% of the data is greater than Q3).

Step8: Percent of data in Plot B less than 85

85 is Q3 (75th percentile) in Plot B. So the percentage of data less than Q3 is 75% (since 75% of the data is at or below Q3).

Answer:

s:

1. Median of Plot A: 65; Median of Plot B: 70
2. Plot with lesser range: Plot A
3. Plot with greater IQR: Plot B
4. Upper quartile of Plot A: 80; Upper quartile of Plot B: 85
5. Lower extreme of Plot A: 45; Lower extreme of Plot B: 40
6. Percent of data in Plot B between 60 and 85: 50%
7. Percent of data in Plot A greater than 80: 25%
8. Percent of data in Plot B less than 85: 75%