0,1,1,1,2,3,4,4,6,6,9\nwhich box - plot correctly represents the data?

0,1,1,1,2,3,4,4,6,6,9\nwhich box - plot correctly represents the data?

0,1,1,1,2,3,4,4,6,6,9\nwhich box - plot correctly represents the data?

Answer

Answer:

To determine the correct box - plot, we need to find the five - number summary (minimum, first quartile $Q_1$, median, third quartile $Q_3$, maximum) of the data set (0,1,1,1,2,3,4,4,4,6,6,9).

  1. Find the minimum and maximum:
    • The minimum value of the data set is (0).
    • The maximum value of the data set is (9).
  2. Find the median:
    • There are (n = 12) data points. The median is the average of the (\frac{n}{2}=6)th and ((\frac{n}{2}+1) = 7)th ordered data - points.
    • The (6)th value is (3) and the (7)th value is (4), so the median (M=\frac{3 + 4}{2}=3.5).
  3. Find the first quartile (Q_1):
    • The lower half of the data set is (0,1,1,1,2,3). There are (n_1=6) data points in the lower half. The first quartile (Q_1) is the average of the (\frac{n_1}{2}=3)rd and ((\frac{n_1}{2}+1)=4)th ordered data - points in the lower half.
    • The (3)rd value is (1) and the (4)th value is (1), so (Q_1 = 1).
  4. Find the third quartile (Q_3):
    • The upper half of the data set is (4,4,4,6,6,9). There are (n_2 = 6) data points in the upper half. The third quartile (Q_3) is the average of the (\frac{n_2}{2}=3)rd and ((\frac{n_2}{2}+1)=4)th ordered data - points in the upper half.
    • The (3)rd value is (4) and the (4)th value is (6), so (Q_3=\frac{4 + 6}{2}=5).

The box - plot should have a minimum at (0), (Q_1) at (1), median at (3.5), (Q_3) at (5), and maximum at (9). We need to visually inspect the box - plots to find the one that matches these values.

Since the box - plot values are not labeled with specific numerical values in the question, we assume that we are looking for a box - plot where the left - hand side of the box (representing (Q_1)) is at (1), the line inside the box (representing the median) is at (3.5), the right - hand side of the box (representing (Q_3)) is at (5), and the end - points of the whiskers are at (0) and (9).

Without seeing the actual box - plots with labeled values, we can't give a definite choice among the options provided. But the steps to determine the correct box - plot are as above.

If we assume that we can visually estimate the positions of the box - plot components: We look for a box - plot where the left end of the box is near (1), the middle line of the box is near (3.5), the right end of the box is near (5), and the whiskers extend to (0) and (9).

If we had to choose based on the general shape and position of the box and whiskers: We need to find the box - plot where the box starts around (1), has a middle line around (3.5), ends around (5), and has whiskers going to (0) and (9).

If we assume the box - plots are drawn to scale and we can estimate the values: We check each box - plot for the correct position of the minimum ((0)), (Q_1) ((1)), median ((3.5)), (Q_3) ((5)), and maximum ((9)).

If we assume the first box - plot has the correct positions for these values:

Answer: The first box - plot (assuming it has the correct minimum at (0), (Q_1) at (1), median at (3.5), (Q_3) at (5), and maximum at (9))

Explanation:

Step1: Calculate minimum

The minimum of (0,1,1,1,2,3,4,4,4,6,6,9) is (0).

Step2: Calculate maximum

The maximum of (0,1,1,1,2,3,4,4,4,6,6,9) is (9).

Step3: Calculate median

With (n = 12), median (M=\frac{3 + 4}{2}=3.5).

Step4: Calculate (Q_1)

For lower half ({0,1,1,1,2,3}), (Q_1 = 1).

Step5: Calculate (Q_3)

For upper half ({4,4,4,6,6,9}), (Q_3 = 5).

Step6: Match with box - plot

Look for box - plot with these values.