Make a box and whisker plot with the following statement:The data show the ages of 13 people attending a dinner party.
37, 42, 44, 46, 47, 49, 51, 53, 54, 55, 57, 61, 63
To create a box and whisker plot for the given data, follow these steps:
Step 1: Arrange the data in ascending order:
37, 42, 44, 46, 47, 49, 51, 53, 54, 55, 57, 61, 63
Step 2: Determine the median (middle value) of the data set:
Since we have 13 data points, the median would be the 7th value when arranged in ascending order. In this case, the median is 51.
Step 3: Determine the lower quartile (Q1):
The lower quartile is the median of the lower half of the data set. In this case, the lower half consists of the first 6 values: 37, 42, 44, 46, 47, and 49. To find the median of these values, we take the average of the 3rd and 4th numbers. So, Q1 = (44 + 46)/2 = 45.
Step 4: Determine the upper quartile (Q3):
The upper quartile is the median of the upper half of the data set. In this case, the upper half consists of the last 6 values: 54, 55, 57, 61, 63, and 51. To find the median of these values, we take the average of the 3rd and 4th numbers. So, Q3 = (57 + 61)/2 = 59.
Step 5: Determine the minimum and maximum values:
The minimum value is the smallest value in the data set, which is 37. The maximum value is the largest value, which is 63.
Step 6: Draw the plot:
Now, we can draw the box and whisker plot using these values: Lowest value (37), Q1 (45), Median (51), Q3 (59), and Highest value (63).
On a number line, draw a vertical line and label it. Then, plot a box from Q1 to Q3, with a horizontal line segment inside representing the median. Draw "whiskers" from the box to the lowest and highest values. Finally, label the plot with the corresponding values.
The box and whisker plot for the given data is as follows:
-------------
| 37 |
| 45 |
| 51 |---Median
| 59 |
| 63 |
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I hope this helps! Let me know if you have any further questions.
To create a box and whisker plot for the given data, you need to organize the data and follow these steps:
1. Arrange the data in ascending order:
37, 42, 44, 46, 47, 49, 51, 53, 54, 55, 57, 61, 63
2. Find the median (middle value) of the data set. Since the number of data points is odd (13), the median is the middle value, which is the 7th value in this case. The median is 49.
3. Find the lower quartile (Q1), which is the median of the lower half of the data. In this case, the lower half is the first 6 values. The median of these values is the 3rd value, which is 44.
4. Find the upper quartile (Q3), which is the median of the upper half of the data. In this case, the upper half is the last 6 values. The median of these values is the 3rd value, which is 54.
5. Calculate the minimum and maximum values. The minimum value is the first value in the data set, which is 37. The maximum value is the last value in the data set, which is 63.
Now that we have all the necessary values, we can create the box and whisker plot:
Step 1: Draw a number line that spans the range of the data.
Step 2: Place a box with a line segment inside it, representing the median. The median (middle value) of the data set is 49. So, on the number line, draw a box with a line segment at 49.
Step 3: Draw two vertical lines (whiskers) from the box, one extending to the minimum value (37) and the other to the maximum value (63).
Step 4: Draw lines from the box to the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is 44, so draw a line from the box to 44. The upper quartile is 54, so draw a line from the box to 54.
Your box and whisker plot should now be complete, showing the values and range of the data set.