Use the following data set to answer this question:
14, 17, 13, 15, 14, 19, 2, 18
What is the interquartile range?
*
4
4.5
2
2.5
To find the interquartile range, we first need to find the lower quartile (Q1) and upper quartile (Q3).
1. Order the data set in ascending order: 2, 13, 14, 14, 15, 17, 18, 19
2. Find the median (middle value) of the lower half of the data set. The lower quartile (Q1) is the median of the lower half. In this case, the lower half is: 2, 13, 14, 14. So, Q1 = (13 + 14)/2 = 13.5
3. Find the median (middle value) of the upper half of the data set. The upper quartile (Q3) is the median of the upper half. In this case, the upper half is: 15, 17, 18, 19. So, Q3 = (17 + 18)/2 = 17.5
4. Finally, calculate the interquartile range (Q3 - Q1): 17.5 - 13.5 = 4.
Therefore, the interquartile range is 4.
Describe the change to the MEAN if 1 is added to the data set below:
4, 12, 7, 0, 5, 2
*
The mean does not change
The mean increases
The mean decreases
To determine the effect of adding 1 to the data set on the mean, we need to calculate the mean for both the original data set and the modified data set.
Original data set: 4, 12, 7, 0, 5, 2
Mean = (4 + 12 + 7 + 0 + 5 + 2) / 6 = 30 / 6 = 5
Modified data set (after adding 1): 5, 13, 8, 1, 6, 3
Mean = (5 + 13 + 8 + 1 + 6 + 3) / 6 = 36 / 6 = 6
Comparing the means of the original and modified data sets, we can see that the mean increases when 1 is added. Thus, the correct answer is: The mean increases.
Describe the shape of this histogram.
*
Captionless Image
Skewed right
Skewed left
Symmetrical
Uniform
Without being able to view the image or receive any information about its shape or distribution, it is not possible to accurately describe the shape of the histogram.
Describe the shape of this histogram.
*
Skewed right
Skewed left
Symmetrical
Uniform
Without any information about the data or the distribution, it is not possible to accurately describe the shape of the histogram.
here
Describe the shape of this histogram.
Skewed right
Skewed left
Symmetrical
Uniform
Without having access to the histogram or any information about the data, it is impossible to describe the shape of the histogram.
To find the interquartile range, follow these steps:
1. Sort the data set in ascending order: 2, 13, 14, 14, 15, 17, 18, 19.
2. Determine the first quartile (Q1): Q1 is the median of the lower half of the data set. In this case, the lower half is {2, 13, 14, 14}. Since there is an even number of values in the lower half, the median is the average of the middle two values, which are 13 and 14. So, Q1 = (13 + 14)/2 = 13.5.
3. Determine the third quartile (Q3): Q3 is the median of the upper half of the data set. In this case, the upper half is {15, 17, 18, 19}. Again, there is an even number of values in the upper half, so the median is the average of the middle two values, which are 17 and 18. Thus, Q3 = (17 + 18)/2 = 17.5.
4. Calculate the interquartile range (IQR): IQR is the difference between Q3 and Q1. Therefore, IQR = Q3 - Q1 = 17.5 - 13.5 = 4.
So, the interquartile range of the given data set {14, 17, 13, 15, 14, 19, 2, 18} is 4.