# Rounding rules for standard deviation and variance relationship

### Stats: Probability Distributions

Aug 17, Rounding Rule for Multiplying and Dividing rounding when you report your results in statistics (for example, the mean or standard deviation). Mean, Variance, and Standard Deviation that this is the population variance, the sample variance, which was the unbiased Only round off the final answer. The rules for significant figures can be summarized as follows: 1. To determine the For addition or subtraction, round off the result to the leftmost decimal place . For When determining the mean and standard deviation based on repeated.

Reporting risk ratios to three significant digits for example leads to the largest ratio below 1 being reported as 0.

- Population and sample standard deviation review
- Stats: Probability Distributions

This is clearly unsatisfactory as they differ in precision by a factor of ten. In this instance a combination of significant digits and decimal places, the rule of four, 11 works best: The rule of four gives three decimal places for risk ratios from 0. Alternatively one can apply the rule with one less significant digit, giving 23 with CI 8 to A suitable rule specifies up to one decimal place and up to two significant digits.

### Math Forum - Ask Dr. Math

When comparing group means or percentages in tables, rounding should not blur the differences between them. This is the basis for the Hopkins two digits rule, 7 whereby the mean has enough decimal places to ensure two significant digits for the SD.

In practice percentages are usually given along with their corresponding frequencies, so precision is less critical as the exact values can be calculated. Recognising the fallibility of decimal places rules means that tables ought not to be restricted to columns of numbers with fixed decimal places, and this adds flexibility when deciding how many decimals to use.

For example measures of variability, eg, standard errors SE s or CIs, need not be as precise as the effect size, particularly if the CI is wide. A useful trick when formatting table columns is to align the numbers by decimal point, which highlights differences in the number of decimal places.

This is particularly useful in columns of risk ratios or p values—see the examples in the table. It is important that any intermediate calculations are carried out to full precision, and that rounding is done only at the reporting stage. This raises the question as to whether the rounded results need extra precision in case they are later included in meta-analyses. But to my mind this confuses two distinct aims—to present the results as accessibly as possible, and to report the results as raw data for meta-analysis.

If the two aims are mutually exclusive then the first has to take priority.

## Too many digits: the presentation of numerical data

But in practice they may not be mutually exclusive—where effect sizes are rounded to two or three significant digits the rounding error variance is likely to be small compared with the inter-study variance, making the rounding imprecision relatively unimportant. The general principle is to use two or three significant digits for effect sizes, and one or two significant digits for measures of variability.

Sum Find the estimated mean or "average" of the data.

**How to Calculate Standard Deviation**

Divide the sum of the data S, found in step 3 by the number of data points found in step 1. Find the squares of the midpoints of each interval range. For each interval range, find the square of the midpoint. Add another column to your table for this I'll put it after the Sum column.

Find the estimated sum-of-the-squares of the data. To find the sum-of-the-squares, multiply the square of the midpoint of each interval range by the frequency of that interval range. For example, the square of the midpoint of the first interval range is Find the estimated mean square of the data. Divide the sum-of-the-squares of the data S2, found in step 6 by the number of data points found in step 1.

Find the estimated variance and standard deviation of the data.

### Population and sample standard deviation review (article) | Khan Academy

To find the variance, square the mean from step 4then subtract it from the mean square. Note that the mean square and the square of the mean are not the same!

Your means, squares, variance and standard deviation are all based on estimations of the actual data. That depends on the accuracy and precision of the original data.

In some scientific fields, there are very specific rules for determining the number of significant figures to leave in an answer, and they can get quite complicated. As a general rule, your final answer should have the same precision i.

So, for example, if I had the data set: