the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. which of the following statements about the box - and - whisker plot below is not true? the midrange of the data set shown is between 80 and 82. both 72 and 99 are values in the set of data. there are the same number of data points in the upper two quartiles and the two lower quartiles. the midrange of the data set shown is 85.5.

Question

Accepted Answer

To solve this, we analyze each option using box - and - whisker plot concepts:

### Step 1: Recall key concepts
- **Midrange**: It is calculated as $\frac{	ext{minimum}+	ext{maximum}}{2}$.
- **Quartiles**: A box - and - whisker plot divides data into four quartiles, each containing approximately 25% of the data points.
- **Whiskers**: They represent the range of the data (excluding outliers), with the left whisker starting at the minimum value and the right whisker ending at the maximum value.

### Step 2: Analyze Option A
From the plot, the minimum value (left whisker start) is 72 and the maximum value (right whisker end) is 99. The midrange is $\frac{72 + 99}{2}=\frac{171}{2}=85.5$. 85.5 is between 80 and 82? No, 85.5 is between 85 and 86. Wait, maybe we misread the minimum and maximum. Wait, looking at the number line: the left whisker starts at 72 (the first vertical line on the left whisker) and the right whisker ends at 99 (the last vertical line on the right whisker). Wait, no, let's check the number line again. The leftmost point of the left whisker is at 72, and the rightmost point of the right whisker is at 99. Then midrange is $\frac{72 + 99}{2}=85.5$. 85.5 is not between 80 and 82. But wait, maybe we made a mistake. Wait, let's check other options first.

### Step 3: Analyze Option B
In a box - and - whisker plot, the whiskers extend to the minimum and maximum values of the data set (excluding outliers). The left whisker starts at 72, so 72 is a data point (the minimum). The right whisker ends at 99, so 99 is a data point (the maximum). So this statement is true.

### Step 4: Analyze Option C
By the definition of a box - and - whisker plot, each quartile contains approximately 25% of the data. So the upper two quartiles (the two quartiles above the median) and the lower two quartiles (the two quartiles below the median) each contain 50% of the data points. So the number of data points in the upper two quartiles and the lower two quartiles is the same. This statement is true.

### Step 5: Analyze Option D
As calculated before, midrange $=\frac{72 + 99}{2}=\frac{171}{2}=85.5$. This statement is true.

Now, going back to Option A. The midrange is 85.5, which is not between 80 and 82. But wait, maybe we misidentified the minimum and maximum. Wait, looking at the number line: the left whisker starts at 72 (the first mark on the left whisker) and the right whisker ends at 99 (the last mark on the right whisker). So the minimum is 72, maximum is 99. Midrange is 85.5. So Option A says "The midrange of the data set shown is between 80 and 82" which is false. But wait, the question is which statement is not true. Wait, maybe we made a mistake. Wait, let's re - evaluate Option A. Wait, maybe the minimum is 72 and maximum is 99, midrange is 85.5. 85.5 is not between 80 and 82. But let's check the other options again.

Wait, Option B: "Both 72 and 99 are values in the set of data." In a box - and - whisker plot, the ends of the whiskers represent the minimum and maximum values of the data set (assuming no outliers). So the left whisker starts at 72, so 72 is the minimum, and the right whisker ends at 99, so 99 is the maximum. So 72 and 99 are in the data set. So this is true.

Option C: "There are the same number of data points in the upper two quartiles and the two lower quartiles." Since the box - and - whisker plot divides the data into four quartiles, each with approximately 25% of the data. So the lower two quartiles (first and second) contain 50% of the data, and the upper two quartiles (third and fourth) contain 50% of the data. So the number of data points in the upper two quartiles and the lower two quartiles is the same. This is true.

Option D: "The midrange of the data set shown is 85.5." Midrange $=\frac{	ext{min}+	ext{max}}{2}=\frac{72 + 99}{2}=\frac{171}{2}=85.5$. This is true.

Option A: "The midrange of the data set shown is between 80 and 82." Since the midrange is 85.5, which is not between 80 and 82, this statement is not true. But wait, the options are:

1. The midrange of the data set shown is between 80 and 82.
2. Both 72 and 99 are values in the set of data.
3. There are the same number of data points in the upper two quartiles and the two lower quartiles.
4. The midrange of the data set shown is 85.5.

Wait, maybe we misread the minimum and maximum. Let's look at the number line again. The left whisker: the first vertical line on the left whisker is at 72, and the right whisker: the last vertical line on the right whisker is at 99. So minimum = 72, maximum = 99. Midrange = (72 + 99)/2 = 85.5. So 85.5 is not between 80 and 82. So Option A is false. But wait, the question is which statement is not true. But let's check Option B again. In a box - and - whisker plot, the whiskers go to the minimum and maximum values (non - outlier data). So 72 is the minimum, 99 is the maximum, so they are in the data set. So Option B is true.

Wait, maybe the error is in Option A. But let's check the midrange calculation again. min = 72, max = 99. (72+99)/2 = 85.5. 85.5 is not between 80 and 82. So Option A is not true. But let's check the other options.

Wait, maybe the minimum is not 72. Wait, the left whisker: the horizontal line of the left whisker starts at 72 (the first vertical tick on the left whisker) and the box starts at 77? Wait, no, the box is between 77 (or 78?) and 90? Wait, the number line: 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100. The left whisker: the vertical line at the start of the left whisker is at 72, then the left whisker goes to the box which starts at 77 (or 78? The box is from, looking at the plot, the left side of the box is at 77 (or 78) and the right side at 90. The left whisker is from 72 to 77 (or 78), and the right whisker from 90 to 99.

So minimum value (the start of the left whisker) is 72, maximum value (the end of the right whisker) is 99.

Midrange = (72 + 99)/2 = 85.5.

Now, let's check each option:

- Option A: Says midrange is between 80 and 82. But 85.5 is not between 80 and 82. So this statement is false.
- Option B: 72 is the minimum (start of left whisker) and 99 is the maximum (end of right whisker), so both are in the data set. True.
- Option C: The data is divided into four quartiles, each with ~25% of data. So upper two quartiles (50% of data) and lower two quartiles (50% of data) have same number of data points. True.
- Option D: Midrange is (72 + 99)/2 = 85.5. True.

So the statement that is not true is "The midrange of the data set shown is between 80 and 82." But wait, the options are presented as radio buttons. Wait, maybe we made a mistake. Wait, let's check the midrange again. If the minimum is 72 and maximum is 99, midrange is 85.5. 85.5 is not between 80 and 82. So Option A is not true. But let's check the other options. Wait, maybe the question is which statement is not true, and the answer is the option "The midrange of the data set shown is between 80 and 82." But let's confirm.

Wait, another way: Let's check the midrange calculation. min = 72, max = 99. (72 + 99)/2 = 85.5. 85.5 is not between 80 and 82. So Option A is false.

But let's check the other options again. Option B: In a box - and - whisker plot, the whiskers extend to the minimum and maximum values (assuming no outliers). So 72 is the minimum, 99 is the maximum, so they are in the data set. True.

Option C: Quartiles divide data into four groups of ~25% each. So two lower quartiles (50% of data) and two upper quartiles (50% of data) have the same number of data points. True.

Option D: Midrange is (72 + 99)/2 = 85.5. True.

So the statement that is not true is "The midrange of the data set shown is between 80 and 82." But wait, the options are:

1. The midrange of the data set shown is between 80 and 82.
2. Both 72 and 99 are values in the set of data.
3. There are the same number of data points in the upper two quartiles and the two lower quartiles.
4. The midrange of the data set shown is 85.5.

So the answer is the option "The midrange of the data set shown is between 80 and 82."

But wait, maybe we made a mistake in the minimum and maximum. Let's re - examine the plot. The left whisker: the first vertical line on the left whisker is at 72, and the right whisker's last vertical line is at 99. So min = 72, max = 99. Midrange = 85.5. So Option A is false.

So the statement that is not true is "The midrange of the data set shown is between 80 and 82."

# Answer: The midrange of the data set shown is between 80 and 82.

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QUESTION IMAGE

Question

Explanation:

Step 1: Recall key concepts

Step 2: Analyze Option A

Step 3: Analyze Option B

Step 4: Analyze Option C

Step 5: Analyze Option D

Answer: