1. Which of the following statements is incorrect? The median is the most a

permaneceerc 2021-10-27 Answered
1. Which of the following statements is incorrect?
The median is the most appropriate measure of central tendency for highly-skewed data distributions.
The variance is always greater than the standard deviation.
A 10% trimmed mean of a given data is solved by removing the largest 10% and smallest 10% of the data, then computing for the mean.
The coefficient of variation is the ratio between the mean and the standard deviation.

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Expert Answer

saiyansruleA
Answered 2021-10-28 Author has 5001 answers
Step 1
Measure of central tendency measures the central or average value of a dataset. Measured of dispersion measures the spread of the data.
Mean, median and mode are some commonly used measures of central tendency. Standard deviation and variance are some commonly used measures of dispersion.
Step 2
Variance is the square of standard deviation. When the standard deviation is less than 1, the variance will be less than standard deviation. So variance is not always greater than standard deviation. So second statement is incorrect.
Median is unaffected by outliers and asymmetry of the data distribution. So median is the appropriate than other measures of central tendency when the data is highly skewed. So first statement is correct.
10% Trimmed mean is obtianed by calculating the mean after removing the largest and smallest 10% of the values. So third statement is correct.
Coefficient of variation is obtained by dividing the standard deviation by mean. Thus it is the ratio between the mean and the standard deviation. So fourth statement is correct.
So only second statement is incorrect and hence it is the answer.
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