1. Explain the measure of center and measure of spread that should be used to compare the following data set with other data sets.
15 10 9 21 18 12 14 11 39 8
17 15 13 19 12 1737 24 13 14
A. The median and the interquartile range should be used because the distribution is skewed right, and there are outliers.
B. The median and the standard deviation should be used because the distribution is symmetric, but there are outliers.
C. The mean and the standard deviation should be used because the distribution is symmetric, and there are no outliers.
D. The median and the range should be used because the distribution is skewed right, and there are no outliers.
A. The median and the interquartile range should be used because the distribution is skewed right, and there are outliers.
1. Compare the differences between when the interquartile range should be used to compare measures of spread and when the range should be used.(1 point)
A. The interquartile range should be used when one or more data sets are skewed or have outliers. The range should be used when all of the data sets do not have any outliers.
B. The interquartile range should be used when all of the data sets do not have outliers. The range should be used when at least one of the data sets has outliers.
C. The interquartile range should only be used when all of the data sets are skewed or have outliers. The range should be used when at most one of the data sets has outliers.
D. The interquartile range should be used when all of the data sets are symmetric and do not have outliers. The range should be used when at least one of the data sets is skewed or has outliers.
B. The interquartile range should be used when at least one of the data sets has outliers. The range should be used when all of the data sets do not have any outliers.
To compare the given data set with other data sets, we need to consider measures of center and measures of spread.
1. The measure of center:
- The median represents the middle value of the data set when it is arranged in ascending or descending order. It is a good choice when the distribution is skewed or there are outliers because it is less affected by extreme values compared to the mean.
2. The measure of spread:
- The interquartile range (IQR) measures the spread of the middle 50% of the data, which makes it a robust measure against outliers. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
Now, let's analyze the given options:
A. The median and the interquartile range should be used because the distribution is skewed right, and there are outliers.
- This option is a valid choice because it suggests using the median (because the distribution is skewed right) and the interquartile range (to account for the outliers).
B. The median and the standard deviation should be used because the distribution is symmetric, but there are outliers.
- This option is incorrect because it assumes the distribution is symmetric, which is not the case. Additionally, the standard deviation is more sensitive to outliers, making it less appropriate in this scenario.
C. The mean and the standard deviation should be used because the distribution is symmetric, and there are no outliers.
- This option is incorrect because it assumes there are no outliers, but in fact, there are outliers present in the data set.
D. The median and the range should be used because the distribution is skewed right, and there are no outliers.
- This option is incorrect because it correctly identifies the skewed right distribution but fails to account for the presence of outliers.
In conclusion, option A is the correct choice as it suggests using the median and the interquartile range, taking into account the skewed right distribution and outliers in the data set.