make a box and whisker plot of the data
21 21 22 20 13 13 27 24
Box and Whisker Plot:
┌────────────────────┐
│ 13 │
│ │ │
│ │ │
│20 21 │
│ │ │
│ │ │
│22 24 │
│ │ │
│ │ │
│ 27 │
└────────────────────┘
To create a box and whisker plot for the given data set: 21, 21, 22, 20, 13, 13, 27, and 24, follow these steps:
Step 1: Arrange the data in ascending order:
13, 13, 20, 21, 21, 22, 24, 27
Step 2: Find the minimum value, maximum value, median, and quartiles of the data:
Minimum value: 13
Maximum value: 27
Median: The median is the middle value when the data is arranged in ascending order. In this case, the median is the average of the two middle values, (21 + 22) / 2 = 21.5.
Quartiles: Quartiles divide the data into four equal parts. There are three quartiles denoted as Q1, Q2, and Q3.
To find Q1, we find the median of the lower half of the data. In this case, the lower half is: 13, 13, 20, and 21. So, the median of the lower half is the average of the two middle values, (13 + 20) / 2 = 16.5.
Q1 = 16.5
To find Q3, we find the median of the upper half of the data. In this case, the upper half is: 21, 22, 24, and 27. So, the median of the upper half is the average of the two middle values, (22 + 24) / 2 = 23.
Q3 = 23
Step 3: Draw a number line representing the data.
Step 4: Plot the minimum value, maximum value, median, Q1, and Q3 on the number line.
Step 5: Draw a box from Q1 to Q3.
Step 6: Draw a line from the middle of the box to the minimum value and another line from the middle of the box to the maximum value. These lines are called whiskers.
Your completed box and whisker plot would look like this:
Minimum value: 13
Q1: 16.5
Median: 21.5
Q3: 23
Maximum value: 27
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13 16.5 21.5 23 27
To create a box and whisker plot for the given data, follow these steps:
1. Arrange the data in ascending order:
13, 13, 20, 21, 21, 22, 24, 27
2. Determine the following values:
- Minimum: the smallest value in the data (13)
- Quartile 1 (Q1): the median of the lower half of the data (13, 13, 20)
- Median (Q2): the median of the entire data set (21)
- Quartile 3 (Q3): the median of the upper half of the data (22, 24, 27)
- Maximum: the largest value in the data (27)
3. Calculate the Interquartile Range (IQR):
IQR = Q3 - Q1
4. Plot the box and whiskers:
- Draw a number line and mark the minimum and maximum values.
- Draw a box from Q1 to Q3, and draw a line in the middle of the box to represent the median (Q2).
- Draw whiskers from the box to the minimum and maximum values.
- Optional: Plot any outliers as dots above or below the whiskers. In this case, there are no outliers.
The resulting box and whisker plot for the given data would look as follows:
┌─────┬─────┬────────┐
│ │ │ │ │ │
13 13 20 21 22 24 27
│ │ │ │ │ │
└─────┴─────┴────────┘
This plot visually represents the distribution and spread of the data. The box encloses the interquartile range (Q1 to Q3), while the line inside the box represents the median. The whiskers extend from the box to the minimum and maximum values.