Make a box and whisker plot of the data, Algebra final exam scores 88, 92, 60, 80, 97, 58, 81, 47, 83, 65, 72, 78, 90, 92, 94, 87, 80, 50, 60, 52
To create a box and whisker plot for the given data, follow these steps:
Step 1: Organize the data in ascending order:
47, 50, 52, 58, 60, 60, 65, 72, 78, 80, 80, 81, 83, 87, 88, 90, 92, 92, 94, 97
Step 2: Find the minimum and maximum values:
The minimum value is 47.
The maximum value is 97.
Step 3: Calculate the quartiles:
- Lower quartile (Q1): Median of the lower half of the data set.
- Median (Q2): Middle value of the data set.
- Upper quartile (Q3): Median of the upper half of the data set.
To find Q1, locate the median of the lower half of the data:
47, 50, 52, 58, 60, 60, 65, 72, 78, 80
Q1 = (58 + 60) / 2 = 59
To find Q2, locate the median of the entire data set:
47, 50, 52, 58, 60, 60, 65, 72, 78, 80, 80, 81, 83, 87, 88, 90, 92, 92, 94, 97
Q2 = (80 + 81) / 2 = 80.5
To find Q3, locate the median of the upper half of the data:
81, 83, 87, 88, 90, 92, 92, 94, 97
Q3 = (88 + 90) / 2 = 89
Step 4: Calculate the Interquartile Range (IQR):
IQR = Q3 - Q1 = 89 - 59 = 30
Step 5: Find any potential outliers:
To identify potential outliers, use the following formula:
Lower fence = Q1 - (1.5 * IQR)
Upper fence = Q3 + (1.5 * IQR)
Lower fence = 59 - (1.5 * 30) = 59 - 45 = 14
Upper fence = 89 + (1.5 * 30) = 89 + 45 = 134
Any values below the lower fence or above the upper fence would be considered outliers. However, in this data set, there are no outliers.
Step 6: Plot the Box and Whisker diagram:
The box represents Q1 to Q3, with a line inside indicating the median (Q2). The whiskers extend from the box to the minimum and maximum values (but do not include outliers if present).
```
| 50 |
|____60___________|
|----------------------| _________90_______|
|----------------------| | |
min---------Q1---Q2----Q3----max
```
In this diagram, the minimum value is 47, the lower quartile (Q1) is 59, the median (Q2) is 80.5, the upper quartile (Q3) is 89, and the maximum value is 97.
To create a box and whisker plot for the given data, follow these steps:
Step 1: Organize the data in ascending order:
47, 50, 52, 58, 60, 60, 65, 72, 78, 80, 80, 81, 83, 87, 88, 90, 92, 92, 94, 97
Step 2: Find the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum values:
Minimum: 47
Q1: 60
Median: 80
Q3: 90
Maximum: 97
Step 3: Calculate the interquartile range (IQR):
IQR = Q3 - Q1
= 90 - 60
= 30
Step 4: Plot the box and whisker plot:
On a number line, draw a horizontal line and label it with the minimum and maximum values (47 and 97, respectively). Use a scale that accommodates the range of the data.
Next, draw a box above the number line starting from Q1 to Q3. Draw a vertical line inside the box to represent the median (Q2).
Finally, draw whiskers (lines) extending from the box to the minimum and maximum values.
Your box and whisker plot will look like this:
| . |
| : |
| . .:.. . |
| . . . . |
| ... . |
---------------------
47 97