# Relationship between variability and standard deviation

### Difference Between Variance and Standard Deviation (with Comparison Chart) - Key Differences

The range is the difference between the largest and smallest values in a set of values. The standard deviation is the square root of the variance. Thus, the. The major difference between variance and standard deviation is that Variance is a numerical value that describes the variability of. The variance and the closely-related standard deviation are measures of how The variance is computed as the average squared deviation of each number by buying your books from Amazon following this link: Books on science and math.

The first part consists of 1 and 2; the second part, 3 and 4; the third part, 5 and 6; and the fourth part, 7 and 8. To compute an interquartile range using this definition, first remove observations from the lower quartile.

Then, remove observations from the upper quartile.

## Standard Deviation and Variance (1 of 2)

Then, from the remaining observations, compute the difference between the largest and smallest values. After we remove observations from the lower and upper quartiles, we are left with: The Variance In a populationvariance is the average squared deviation from the population mean, as defined by the following formula: Observations from a simple random sample can be used to estimate the variance of a population.

For this purpose, sample variance is defined by slightly different formula, and uses a slightly different notation: Using this formula, the sample variance can be considered an unbiased estimate of the true population variance. Therefore, if you need to estimate an unknown population variance, based on data from a simple random sample, this is the formula to use.

The Standard Deviation The standard deviation is the square root of the variance. Thus, the standard deviation of a population is: Statisticians often use simple random samples to estimate the standard deviation of a population, based on sample data.

Given a simple random sample, the best estimate of the standard deviation of a population is: Effect of Changing Units Sometimes, researchers change units minutes to hours, feet to meters, etc. Here is how measures of variability are affected when we change units. If you add a constant to every value, the distance between values does not change.

### Measures of Variability

As a result, all of the measures of variability range, interquartile range, standard deviation, and variance remain the same. On the other hand, suppose you multiply every value by a constant. This has the effect of multiplying the range, interquartile range IQRand standard deviation by that constant.

It has an even greater effect on the variance. The range is simply the highest score minus the lowest score. What is the range of the following group of numbers: The range is 8. What is the range? The highest number is 99 and the lowest number is 23, so 99 - 23 equals 76; the range is Now consider the two quizzes shown in Figure 1.

On Quiz 1, the lowest score is 5 and the highest score is 9. Therefore, the range is 4.

### Variability in Statistics

The range on Quiz 2 was larger: Therefore the range is 6. It is computed as follows: The interquartile range is therefore 2. For Quiz 2, which has greater spread, the 75th percentile is 9, the 25th percentile is 5, and the interquartile range is 4. Recall that in the discussion of box plotsthe 75th percentile was called the upper hinge and the 25th percentile was called the lower hinge.

Using this terminology, the interquartile range is referred to as the H-spread. A related measure of variability is called the semi-interquartile range. The semi-interquartile range is defined simply as the interquartile range divided by 2. If a distribution is symmetric, the median plus or minus the semi-interquartile range contains half the scores in the distribution.

Variance Variability can also be defined in terms of how close the scores in the distribution are to the middle of the distribution. Using the mean as the measure of the middle of the distribution, the variance is defined as the average squared difference of the scores from the mean.

• How to Measure Variability
• Difference Between Variance and Standard Deviation