Why is variance as a measure of variability preferred to the range?

For normal distributions, all measures can be used. The standard deviation and variance are preferred because they take your whole data set into account, but this also means that they are easily influenced by outliers. For skewed distributions or data sets with outliers, the interquartile range is the best measure.

Why is the range not the best measure of variability?

The range is a poor measure of variability because it is very insensitive. By insensitive, we mean the range is unaffected by changes to any of the middle scores. As long as the highest score (i.e., 6) and the lowest score (i.e., 0) do not change, the range does not change.

What is the better measure of variability?

The interquartile range is the best measure of variability for skewed distributions or data sets with outliers. Because it’s based on values that come from the middle half of the distribution, it’s unlikely to be influenced by outliers.

Why would it be better to report the variance or standard deviation than the range?

The smaller your range or standard deviation, the lower and better your variability is for further analysis. The range is useful, but the standard deviation is considered the more reliable and useful measure for statistical analyses. In any case, both are necessary for truly understanding patterns in your data.

Why are measures of variability important?

Why do you need to know about measures of variability? You need to be able to understand how the degree to which data values are spread out in a distribution can be assessed using simple measures to best represent the variability in the data.

What is the difference between variability and variance?

Variability means “lack of consistency”, and it measures how much the data varies. Variance is the average squared deviation of a random variable from its mean.

Is variance the measure of variability?

In statistics, variance measures variability from the average or mean. It is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and finally dividing the sum of the squares by the number of values in the data set.

Is variance a measure of variability?

Why standard deviation is considered a more useful measure of dispersion as compared to variance?

Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. SD is the square root of sum of squared deviation from the mean divided by the number of observations. The other advantage of SD is that along with mean it can be used to detect skewness.

Why is the variance important?

Variance is an important metric in the investment world. Variability is volatility, and volatility is a measure of risk. It helps assess the risk that investors assume when they buy a specific asset and helps them determine whether the investment will be profitable.