Alexa records the total number of points scored in two games by 10 players on her basketball team.
28, 13, 4, 8, 15, 10, 22, 7, 11, 15
Describe a Box plot, that represents the data.
A box plot to represent the given data would have the following characteristics:
- The minimum value in the dataset is 4.
- The first quartile (Q1) is 8.
- The median (Q2) is 13.5.
- The third quartile (Q3) is 17.5.
- The maximum value in the dataset is 28.
The box plot would have a vertical line representing the minimum value, which would be connected to a box. The bottom of the box would be Q1 (8), the middle line within the box would be Q2 (13.5), and the top of the box would be Q3 (17.5). Above the box, there would be a vertical line representing the maximum value (28). Additionally, there might be a few individual points or outliers represented as dots outside the box plot, if any exist in the given dataset.
To construct a box plot that represents the given data, follow these steps:
Step 1: Order the data in ascending order:
4, 7, 8, 10, 11, 13, 15, 15, 22, 28
Step 2: Find the median (middle value) of the data set:
Median = (11 + 13) / 2 = 12
Step 3: Find the lower quartile (Q1), which is the median of the lower half of the data:
Lower half = 4, 7, 8, 10, 11
Lower quartile (Q1) = (8 + 10) / 2 = 9
Step 4: Find the upper quartile (Q3), which is the median of the upper half of the data:
Upper half = 13, 15, 15, 22, 28
Upper quartile (Q3) = (15 + 22) / 2 = 18.5
Step 5: Find the interquartile range (IQR), which is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 18.5 - 9 = 9.5
Step 6: Calculate the lower limit (Q1 - 1.5 * IQR):
Lower limit = 9 - 1.5 * 9.5 = 9 - 14.25 = -5.25
Step 7: Calculate the upper limit (Q3 + 1.5 * IQR):
Upper limit = 18.5 + 1.5 * 9.5 = 18.5 + 14.25 = 32.75
The box plot can now be constructed using the following information:
- The minimum value is 4.
- The lower quartile (Q1) is 9.
- The median is 12.
- The upper quartile (Q3) is 18.5.
- The maximum value is 28.
- The lower whisker extends from the minimum value to the lower limit (-5.25).
- The upper whisker extends from the maximum value to the upper limit (32.75).
- The box is drawn from Q1 to Q3.
- The median line is drawn through the box.
With this information, you can construct a box plot that represents the given data.