make a box-and-whisker plot of the data 21,21,22,20,13,13,27,24
Settle down please oobleck. We're just trying to get help. A teacher that teaches in a brick and mortar school can't answer a student's question with "google it." I understand this is different but google doesn't always provide the answer.
To create a box-and-whisker plot of the given data (21, 21, 22, 20, 13, 13, 27, 24), follow these steps:
Step 1: Order the data in ascending order:
13, 13, 20, 21, 21, 22, 24, 27
Step 2: Find the minimum and maximum values:
Minimum value = 13
Maximum value = 27
Step 3: Find the median (second quartile):
Since there are 8 data points, the median will be the average of the 4th and 5th values.
Median = (21 + 21) / 2 = 21
Step 4: Find the lower quartile (Q1):
Since there are an even number of data points in the lower half, Q1 will be the average of the 2nd and 3rd values.
Q1 = (13 + 20) / 2 = 16.5
Step 5: Find the upper quartile (Q3):
Since there are an even number of data points in the upper half, Q3 will be the average of the 6th and 7th values.
Q3 = (22 + 24) / 2 = 23
Step 6: Calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 23 - 16.5 = 6.5
Step 7: Plot the box-and-whisker plot:
Using the minimum, Q1, median, Q3, and maximum values, draw a number line.
Mark the minimum and maximum values with whiskers.
Draw a box from Q1 to Q3, with a horizontal line inside to represent the median.
Box-and-whisker plot:
┌───────┬──────────────┬─────┐
│ │ 21 │ │
─────┼───────┼──────────────┼─────┼──────
│ Q1 │ 20 │ │
─────┼───────┼──────────────┼─────┼──────
│ │ 13 │ 21 │
└───────┴──────────────┴─────┘
The values outside of the box represent the minimum (13) and the maximum (27) values. The line inside the box represents the median (21), and the box itself represents the interquartile range (16.5 to 23).
To create a box-and-whisker plot for the given data set (21, 21, 22, 20, 13, 13, 27, 24), follow these steps:
Step 1: Sort the data in ascending order:
13, 13, 20, 21, 21, 22, 24, 27
Step 2: Determine the five-number summary:
- Minimum: 13
- First quartile (Q1): The median of the lower half of the data set, which is 13 and 20: (13 + 20) / 2 = 16.5
- Median (Q2): The middle value in the ordered data set, which is 21
- Third quartile (Q3): The median of the upper half of the data set, which is 22 and 24: (22 + 24) / 2 = 23
- Maximum: 27
Step 3: Calculate any outliers:
An outlier is typically defined as a data point that is more than 1.5 times the interquartile range (Q3 - Q1) away from either Q1 or Q3. Calculate the interquartile range:
IQR = Q3 - Q1 = 23 - 16.5 = 6.5
Lower limit for outliers: Q1 - (1.5 * IQR)
Upper limit for outliers: Q3 +(1.5 * IQR)
Step 4: Create the box-and-whisker plot:
Draw a number line and mark the minimum, Q1, median, Q3, and maximum values. Then, draw a box connecting Q1 and Q3, and draw a line through the box to represent the median. Finally, add whiskers extending from the box to the minimum and maximum, excluding any outliers.
Here is the box-and-whisker plot for the given data set:
| 13
|--------------------------
| 20
|--------------------------
| 21
|--------------------------
| 22
|--------------------------
| 24
|--------------------------
| 27
ok, now what?
where do you have trouble? I'm sure your text has examples.
google can provide many more.