draw a box-and-whisker plot for the following set of data. 62,76,41,87,60,42,47,69,65.
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To draw a box-and-whisker plot for the given set of data: 62, 76, 41, 87, 60, 42, 47, 69, 65, follow these steps:
Step 1: Order the data set in ascending order:
41, 42, 47, 60, 62, 65, 69, 76, 87
Step 2: Find the minimum and maximum values:
The minimum value is 41, and the maximum value is 87.
Step 3: Find the median (middle value):
The median is the middle value in the ordered data set. In this case, we have 9 data points, so the median is the value at position (9 + 1) / 2 = 5th position.
The median is 62.
Step 4: Find the lower and upper quartiles:
The lower quartile, Q1, is the median of the lower half of the data. In this case, we have 9 data points, so the lower half is the first 4 data points. The median of these 4 data points is at position (4 + 1) / 2 = 2.5th position.
Q1 is the average of the 2nd and 3rd values, which gives us: (42 + 47) / 2 = 44.5
The upper quartile, Q3, is the median of the upper half of the data. In this case, the upper half is the last 4 data points. The median of these 4 data points is at position (4 + 1) / 2 = 2.5th position.
Q3 is the average of the 6th and 7th values, which gives us: (65 + 69) / 2 = 67
Step 5: Find the Interquartile Range (IQR):
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 67 - 44.5 = 22.5
Step 6: Draw the box-and-whisker plot:
On a number line, label the minimum value (41), Q1 (44.5), the median (62), Q3 (67), and the maximum value (87).
Draw a box that extends from Q1 to Q3, with a vertical line inside the box at the level of the median.
Finally, draw a vertical line extending from the box to the minimum value (41) and another vertical line extending from the box to the maximum value (87).
Your box-and-whisker plot should look like this:
| |_______________
41 | 44.5 | 62 | 67 | 87
| |_______________
That's it! You have successfully drawn a box-and-whisker plot for the given set of data.
To draw a box-and-whisker plot for a given set of data, you need to follow these steps:
1. Arrange the data in ascending order: 41, 42, 47, 60, 62, 65, 69, 76, 87.
2. Find the minimum (smallest) value: The minimum value in this data set is 41.
3. Find the maximum (largest) value: The maximum value in this data set is 87.
4. Calculate the median, which is the middle value when the data set is in ascending order. In this case, the median is the average of the two middle values: (62 + 65) / 2 = 127 / 2 = 63.5.
5. Divide the data into two halves: the lower half and the upper half. The lower half includes the minimum value, the values below the median (41, 42, 47, 60, 62), and the upper half contains the values above the median (65, 69, 76, 87).
6. Calculate the lower quartile (Q1), which is the median of the lower half. In this case, the lower quartile is the average of the two middle values of the lower half: (42 + 47) / 2 = 89 / 2 = 44.5.
7. Calculate the upper quartile (Q3), which is the median of the upper half. In this case, the upper quartile is the average of the two middle values of the upper half: (76 + 87) / 2 = 163 / 2 = 81.5.
Now, we have all the necessary values to draw the box-and-whisker plot:
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41 62 65 76 87
The box-and-whisker plot consists of a box that represents the middle 50% of the data (from Q1 to Q3), with a line inside the box representing the median. Whiskers extend from the box to the minimum and maximum values.