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The data below represents the number of essays that students in Mr. Ji's class wrot...

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Problem

The data below represents the number of essays that students in Mr. Ji's class wrote. 2, 3, 5, 5, 6, 7, 8, 8, 11. Which box plot correctly summarizes the data?

Answer

C

Step-by-step solution

  1. Order the data: The given data set is: $2, 3, 5, 5, 6, 7, 8, 8, 11$. The data is already in ascending order.
  1. Find the minimum and maximum: The minimum value is the smallest number in the data set, which is $2$. The maximum value is the largest number in the data set, which is $11$. These will be the endpoints of the whiskers on the box plot.
  1. Find the median (Q2): The median is the middle value of the data set. Since there are $9$ data points (an odd number), the median is the $(9+1)/2 = 5$th value. The 5th value is $6$. So, the median is $6$.
  1. Find the first quartile (Q1): Q1 is the median of the lower half of the data. The lower half of the data (excluding the median) is $2, 3, 5, 5$. The median of these four numbers is the average of the 2nd and 3rd values: $(3+5)/2 = 4$. So, Q1 is $4$.
  1. Find the third quartile (Q3): Q3 is the median of the upper half of the data. The upper half of the data (excluding the median) is $7, 8, 8, 11$. The median of these four numbers is the average of the 2nd and 3rd values: $(8+8)/2 = 8$. So, Q3 is $8$.

6. Construct the box plot:
- The minimum is $2$ (left whisker).
- Q1 is $4$ (left edge of the box).
- The median (Q2) is $6$ (line inside the box).
- Q3 is $8$ (right edge of the box).
- The maximum is $11$ (right whisker).

7. Compare with the given box plots:
- Box plot A: Minimum $2$, Q1 $4$, Median $6$, Q3 $9$, Maximum $12$. Incorrect.
- Box plot B: Minimum $2$, Q1 $3$, Median $6$, Q3 $7$, Maximum $11$. Incorrect.
- Box plot C: Minimum $2$, Q1 $4$, Median $6$, Q3 $8$, Maximum $11$. Correct.