What fraction of the data 14 8 13 20 15 17 1 12 18 10 is greater then 13.5
please make a box and whisker plot
There are 10 numbers. Five of these numbers are greater than 13.5. What fraction is that?
you are no help
5/10 = ?
what the heck is Whisker Plot.
Kaitlyn, it is to show the distrubutions of the data set
To determine the fraction of the data greater than 13.5, let's first sort the data in ascending order:
1, 8, 10, 12, 13, 14, 15, 17, 18, 20
Next, we can create a box and whisker plot to visualize the distribution of the data. A box and whisker plot consists of a box, which represents the interquartile range (IQR), and two whiskers, which represent the minimum and maximum values of the data.
1. Find the median: The median is the middle value of the sorted data set. In this case, since we have 10 data points, the median is the average of the two middle values, which are 13 and 14. Therefore, the median is (13 + 14) / 2 = 13.5.
2. Find the lower quartile (Q1): The lower quartile is the median of the lower half of the data. In this case, the lower half of the data is 1, 8, 10, 12, and 13. To find the median of this subset, we take the average of the two middle values, which are 10 and 12. Therefore, Q1 is (10 + 12) / 2 = 11.
3. Find the upper quartile (Q3): The upper quartile is the median of the upper half of the data. In this case, the upper half of the data is 14, 15, 17, 18, and 20. To find the median of this subset, we take the average of the two middle values, which are 17 and 18. Therefore, Q3 is (17 + 18) / 2 = 17.5.
4. Find the interquartile range (IQR): The IQR is the difference between Q3 and Q1. Therefore, IQR = Q3 - Q1 = 17.5 - 11 = 6.5.
5. Determine the minimum and maximum values: The minimum value is the smallest value in the data set, which is 1. The maximum value is the largest value in the data set, which is 20.
Now, we can construct the box and whisker plot using these values:
| + + |
| *|__ ________________|* |
-----|---+---+-------------------+---+------|-----
1 11.0 13.5 20
In the plot above, the box represents the interquartile range (IQR), the horizontal line within the box represents the median, the whisker on the left represents the minimum value, and the whisker on the right represents the maximum value.
To determine the fraction of the data greater than 13.5, we need to count the number of data points that are greater than 13.5. In this case, there are 4 data points (14, 15, 17, and 18) that are greater than 13.5.
Therefore, the fraction of the data that is greater than 13.5 is 4/10 or 2/5.