Which box-and-whisker plot matches the data?
27, 33, 20, 13, 27, 37, 31, 37, 27, 18, 31, 18
A. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from between 18 and 20 to between 30 and 32. There is a division and a point between 26 and 27. The left whisker extends from a point between 12 and 14 to a point between 18 and 20. The right whisker extends from a point between 30 and 32 to 36.
B. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from between 18 and 20 to 32. There is a division and a point between 26 and 27. The left whisker extends from a point between 12 and 14 to the box between 18 and 20. The right whisker extends from 32 to a point between 36 and 38.
C. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from between 18 and 20 to between 30 and 32. There is a division and a point between 22 and 24. The left whisker extends from a point between 12 and 14 to the box between 18 and 20. The right whisker extends from the box between 30 and 32 and extends to 38.
D. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2.The box extends from 18 to a point between 30 and 32. There is a division and a point at 24. The left whisker extends from 12 to 18. The right whisker extends from the box at a point between 30 and 32 to 36.
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The correct answer is C. A box-and-whisker plot is shown above a number line that spans from 10 to 40. It is marked in increments of 2. The box extends from between 18 and 20 to between 30 and 32. There is a division and a point between 22 and 24. The left whisker extends from a point between 12 and 14 to the box between 18 and 20. The right whisker extends from the box between 30 and 32 and extends to 38.
To determine which box-and-whisker plot matches the given data, we need to analyze the data points and their corresponding positions on the number line.
The given data points are: 27, 33, 20, 13, 27, 37, 31, 37, 27, 18, 31, 18.
The first step is to find the minimum and maximum values in the dataset to determine the range. In this case, the minimum value is 13, and the maximum value is 37.
The second step is to find the median, which is the middle value of the dataset. To find the median, we first need to arrange the data points in ascending order: 13, 18, 18, 20, 27, 27, 27, 31, 31, 33, 37, 37. Because there are 12 data points, the median will be the average of the 6th and 7th values, which are both 27.
The third step is to find the lower quartile (Q1) and upper quartile (Q3). Q1 represents the median of the lower half of the data points, and Q3 represents the median of the upper half of the data points. To find Q1 and Q3, we need to find the median of the lower and upper halves of the dataset, respectively.
For the lower half of the data, which consists of 13, 18, 18, 20, 27, and 27, the median will be the average of the 3rd and 4th values, which are 18 and 20. Therefore, Q1 is 19.
For the upper half of the data, which consists of 31, 31, 33, 37, and 37, the median will be the average of the 3rd and 4th values, which are both 33. Therefore, Q3 is 33.
Now that we have the minimum (13), Q1 (19), median (27), Q3 (33), and maximum (37), let's compare these values with the four provided box-and-whisker plots:
A. The box extends from between 18 and 20 to between 30 and 32. Q1 (19) and Q3 (33) are correctly represented. However, the left whisker extends from a point between 12 and 14, which is incorrect.
B. The box extends from between 18 and 20 to 32. Q1 (19) and Q3 (33) are correctly represented. The left whisker extends from a point between 12 and 14 to the box, which is correct. However, the right whisker extends to a point between 36 and 38, which is incorrect.
C. The box extends from between 18 and 20 to between 30 and 32. Q1 (19) and Q3 (33) are correctly represented. However, there is a division and a point between 22 and 24, which is incorrect. The right whisker extends from the box to 38, which is incorrect.
D. The box extends from 18 to a point between 30 and 32. Q1 (19) and Q3 (33) are correctly represented. The left whisker extends from 12 to 18, which is correct. The right whisker extends from the box to 36, which is correct. The point at 24 is also correctly shown as a division on the number line.
Thus, the correct box-and-whisker plot that matches the given data is Option D.