Which measure of central tendency and which measure of variation should be used with a heavily skewed distribution.
A. The mean and standard deviation
B. The median and standard deviation
C. The mode and interquartile range
D. The mean and interquartile range
E. The median and interquartile range
I know that for a heavily skewed distribution, you would use median to eliminate any outliers that would change the data, but what variation would you use?
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Use the mean to describe an entire set of observations with a single value representing the center of the data. Many statistical analyses use the mean as a standard reference point. The mean is the sum of all observations divided by the number of observations.
For example, the waiting time (in minutes) of five customers in a bank are: 3, 2, 4, 1, and 2. The mean waiting time is:
On average, a customer waits 2.4 minutes for service at the bank.
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Use the median to describe an entire set of observations with a single value representing the center of the data. Half of the observations are above the median, half are below it. It is determined by ranking the data and finding observation number [N + 1] / 2. If there are an even number of observations, the median is extrapolated as the value midway between that of observation numbers N / 2 and [N / 2] + 1.
For this ordered data, the median is 13. That is, 50% of the values are less than or equal to 13, and 50% of the values are greater than or equal to 13.
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The mode is the value that occurs most frequently in a set of observations. Minitab also displays how many data points equal the mode. Mode may be used with mean and median to give an overall characterization of your data distribution. While the mean and median require a calculation, the mode is found simply by counting the number of times each value occurs in a data set.
Identifying the mode can help you understand your distribution. A distribution with more than one mode may indicate that you actually have sampled from a mixed population. For example, you may have collected wait time data on customers who are cashing checks and customers who are applying for home equity loans together. To better understand your data, these two cases should be collected separately. If you have more than two modes, the distribution is multimodal.
okay but then what about the variations like what is the answer?
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