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a box and whisker plot as shown.
which information is correct for this box - and - whisker plot?
one - half of the data is between 130 and 140.
one - half of the data is between 120 and 140.
the median is 108 and the interquartile range is 24.
the median is 120 and the interquartile range is 40.

Question

Accepted Answer

# Explanation:
## Step1: Recall box - and - whisker plot properties
In a box - and - whisker plot, the box represents the interquartile range (IQR). The line inside the box is the median. Half of the data lies within the box (i.e., between $Q_1$ and $Q_3$). The whiskers extend to the minimum and maximum values.
## Step2: Analyze each option
- **Option 1**: One - half of the data is between $Q_1$ and $Q_3$. From the plot, we can see that the box starts at $108$ (approximate $Q_1$) and ends at $128$ (approximate $Q_3$). The range $130 - 140$ is not the interquartile range.
- **Option 2**: The range $120 - 140$ is not the interquartile range. The interquartile range is between $Q_1$ and $Q_3$ (not $120$ as a starting point).
- **Option 3**: If the median ($Q_2$) was $108$, the line inside the box would be at $108$. But from the plot, the line inside the box (median) is at $120$. The interquartile range $IQR=Q_3 - Q_1$. If $Q_1 = 108$ and $Q_3 = 128$, $IQR=128 - 108=20
eq24$.
- **Option 4**: The line inside the box (median) is at $120$. If $Q_1 = 108$ and $Q_3 = 128$, $IQR = 128-108 = 20$ (incorrect calculation in option). Wait, re - check:
    - The left - hand side of the box ( $Q_1$) is at $108$, the median ($Q_2$) is at $120$, and the right - hand side of the box ($Q_3$) is at $128$. The minimum value is $100$ and the maximum value is $140$.
    - The interquartile range $IQR=Q_3 - Q_1$. If we assume $Q_1 = 108$ and $Q_3 = 128$, $IQR = 20$ (wrong). But if we consider the correct interpretation:
    - The box starts at $108$ ($Q_1$), median ($Q_2$) at $120$, box ends at $128$ ($Q_3$). Half of the data is between $Q_1$ and $Q_3$ (i.e., $108$ and $128$). But if we consider the overall data:
    - The median is $120$. The interquartile range $IQR = Q_3 - Q_1$. If $Q_1=108$ and $Q_3 = 128$, $IQR=20$ (error in option). Wait, no:
    - Let's re - evaluate. The left end of the box ( $Q_1$) is $108$, the median ($Q_2$) is $120$, the right end of the box ($Q_3$) is $128$.
    - One - half of the data is between $Q_1$ and $Q_3$ (i.e., $108$ and $128$). But if we consider the options again:
    - The median is the middle value. In a box - and - whisker plot, the line inside the box is the median. Here the line is at $120$. The interquartile range $IQR = Q_3 - Q_1$. If $Q_1 = 108$ and $Q_3=128$, $IQR = 20$ (incorrect in options). But if we assume a mis - read of the plot (maybe $Q_1 = 108$, $Q_3 = 128$ is wrong). Wait, no:
    - Wait, another approach:
    - The box - and - whisker plot divides the data into four equal parts. The median ($Q_2$) splits the data into two halves. The lower half is from the minimum to $Q_2$ and the upper half is from $Q_2$ to the maximum.
    - If we consider the position of the line inside the box (median) is at $120$.
    - The interquartile range: assume $Q_1 = 108$ and $Q_3 = 128$ (by visual inspection of the box). $IQR=128 - 108=20$ (wrong in options). But if we consider the following:
    - The first option: One - half of the data is between $Q_1$ and $Q_3$. If $Q_1 = 108$ and $Q_3 = 128$, it's not $130 - 140$.
    - The second option: One - half of the data is between $Q_1$ and $Q_3$ (not $120 - 140$).
    - The third option: Median is not $108$.
    - The fourth option: If we assume that there was a mis - scaling (but based on the number line):
        - The median (the line inside the box) is at $120$. The interquartile range: if $Q_1 = 108$ and $Q_3 = 128$, $IQR = 20$ (wrong). But if we consider that the left end of the box ( $Q_1$) is $108$, the median ($Q_2$) is $120$, and assume that the problem has a typo in $IQR$ calculation (maybe a wrong visual read). But among the options, the only one with the correct median ($120$) is the fourth option. Maybe the $IQR$ was miscalculated in the problem's option creation (if we assume $Q_1 = 100$ (wrong, because the box starts at $108$) no. Wait, no:
        - The correct property is that the median ($Q_2$) divides the data into two equal parts. So half of the data is between the minimum and $Q_2$ and half is between $Q_2$ and the maximum. If the median ($Q_2$) is $120$, half of the data is between $120$ and $140$ (assuming the maximum is $140$)

# Answer:
One - half of the data is between $120$ and $140$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall box - and - whisker plot properties

Step2: Analyze each option

Answer: