To determine the percentage of the data values between 45 and 75 in the box-and-whisker plot, we need to examine the interquartile range (IQR).
The box-and-whisker plot typically displays the following components:
- The box represents the interquartile range (IQR), which spans from the first quartile (Q1) to the third quartile (Q3).
- The line inside the box represents the median (Q2).
- The whiskers extend from the ends of the box to the minimum and maximum values within 1.5 times the IQR from the quartiles.
To find the percentage of data values between 45 and 75, we first need to identify the quartiles from the box-and-whisker plot. Let's assume the box represents the interquartile range.
Let Q1 be the first quartile (the lower end of the box), and Q3 be the third quartile (the upper end of the box).
Then, the interquartile range (IQR) = Q3 - Q1.
Now, we need to see how much of this range is between 45 and 75.
If we denote Q1 = 45 and Q3 = 75, then the IQR = 75 - 45 = 30.
To find the percentage of data values between 45 and 75, we calculate the proportion of the IQR that falls between these two values:
\[ \text{Percentage} = \frac{\text{Length between 45 and 75}}{\text{Total IQR}} \times 100\% \]
\[ \text{Percentage} = \frac{75 - 45}{30} \times 100\% \]
\[ \text{Percentage} = \frac{30}{30} \times 100\% \]
\[ \text{Percentage} = 100\% \]
So, 100% of the data values are between 45 and 75.