1. Which of the following statements is not true?The most appropriate measure of central tendency for highly-skewed data distributions is the medianThe variance is always greater than the standard deviation.&nbsp;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.&nbsp;The coefficient of variation is the ratio between the mean and the standard deviation.

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1. Which of the following statements is not true?The most appropriate measure of central tendency for highly-skewed data distributions is the medianThe variance is always greater than the standard deviation.&amp;nbsp;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.&amp;nbsp;The coefficient of variation is the ratio between the mean and the standard deviation.

saiyansruleA · Accepted Answer

Step 1&amp;nbsp;The central tendency of a dataset can be measured by finding the average value of the data. Measured of dispersion measures the spread of the data.&amp;nbsp;Mean, median and mode are some commonly used measures of central tendency. Standard deviation and variance are some commonly used measures of dispersion.&amp;nbsp;Step 2&amp;nbsp;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.&amp;nbsp;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.&amp;nbsp;10% Trimmed mean is obtianed by calculating the mean after removing the largest and smallest 10% of the values. So third statement is correct.&amp;nbsp;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.&amp;nbsp;So only second statement is incorrect and hence it is the answer.

Eliza Beth13 · Accepted Answer

1. The most appropriate measure of central tendency for highly-skewed data distributions is the median.This statement is true. The median is less affected by extreme values in highly-skewed distributions, making it a more appropriate measure of central tendency.2. The variance is always greater than the standard deviation.This statement is false. The variance is the average of the squared differences from the mean, while the standard deviation is the square root of the variance. Since the standard deviation involves taking the square root, it is always smaller than or equal to the variance.3. A 10% trimmed mean of a given data is solved by removing the largest 10% and smallest 10% of the data, then computing the mean.This statement is true. The 10% trimmed mean involves discarding a certain percentage of the extreme values (both largest and smallest) and then calculating the mean of the remaining values.4. The coefficient of variation is the ratio between the mean and the standard deviation.This statement is true. The coefficient of variation is a relative measure of variability and is calculated as the ratio of the standard deviation to the mean.Therefore, the statement that is not true is statement 2: &#039;The variance is always greater than the standard deviation.&#039;Answer:&amp;nbsp;Statement&amp;nbsp;2&amp;nbsp;is&amp;nbsp;not&amp;nbsp;true.

madeleinejames20 · Accepted Answer

Answer:Statement 1: TrueStatement 2: FalseStatement 3: FalseStatement 4: TrueExplanation:Let&#039;s evaluate each statement one by one:1. The most appropriate measure of central tendency for highly-skewed data distributions is the median.The statement is true. For highly-skewed data distributions, the mean can be heavily influenced by outliers, making it an inappropriate measure of central tendency. The median, on the other hand, is less affected by extreme values and provides a better representation of the typical value in skewed distributions.2. The variance is always greater than the standard deviation.The statement is false. The variance is calculated as the average of the squared deviations from the mean, while the standard deviation is the square root of the variance. Since the variance involves squaring the deviations, it tends to yield larger values compared to the standard deviation. However, if the data has a very small range or is very close to the mean, the variance can be smaller than the standard deviation.3. 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 statement is false. A 10% trimmed mean involves removing a certain percentage of extreme values from both tails of the data, and then computing the mean of the remaining values. In this case, it would involve removing the largest 10% and the smallest 10% of the data. However, the remaining data points are not averaged; instead, the mean is computed using the trimmed dataset.4. The coefficient of variation is the ratio between the mean and the standard deviation.The statement is true. The coefficient of variation (CV) is a measure of relative variability and is calculated as the ratio between the standard deviation and the mean. It is often expressed as a percentage by multiplying the ratio by 100.

nick1337 · Accepted Answer

Statement 1: The most appropriate measure of central tendency for highly-skewed data distributions is the median.Solution: False. The most appropriate measure of central tendency for highly-skewed data distributions is the text{mode}, not the median.Statement 2: The variance is always greater than the standard deviation.Solution: False. The variance is not always greater than the standard deviation. The standard deviation is the square root of the variance, so the standard deviation is always equal to or smaller than the variance.Statement 3: 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.Solution: True. A 10% trimmed mean is indeed computed by removing the largest 10% and smallest 10% of the data and then calculating the mean of the remaining data points.Statement 4: The coefficient of variation is the ratio between the mean and the standard deviation.Solution: False. The coefficient of variation is calculated as the ratio of the standard deviation to the mean, not the other way around. It is expressed as a percentage and provides a measure of relative variability.

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

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