There is no direct relationship between mean and SD because the mean is simple average of algebraic sum of data whereas the SD is obtained from the average of the square of data. Also SD is obtained by removing mean from the data. Statistically, there is no limit on SD with respect to mean.

Yes, for example a standard normal distribution has a mean of 0 and a standard deviation of 1. Having only positive numbers the set (1,2,3,12) has a mean of 4 and a SD greater than 5.

yes it may be. It depends on the dataset used for study

There is no direct relationship between mean and SD because the mean is simple average of algebraic sum of data whereas the SD is obtained from the average of the square of data. Also SD is obtained by removing mean from the data. Statistically, there is no limit on SD with respect to mean.

Dear Ali

As Dr Verma mentioned it depends on the data set you are analyzing.

It's not bad or good because there is no direct relation between them.

Hii

Yes Mr. Ali Al-Awadhi this could be happen when your data have negative sign. As example when subtract pre test from post test. The following data is an example : -1, 0, -2, 2, -4, 1

the arithmetic mean is -0.67 and standard deviation is 2.16

The answer is yes. (1) Both the population or sample MEAN can be negative or non-negative while the SD must be a non-negative real number.

(2) The Mean reflects the location while the SD reflects the dispersion. MEAN can be larger or smaller than SD. Please see the following examples: MEAN > SD: 2,2,2,2,2

MEAN < SD: -1000, -500, 1, 2000

There are a number of good answers to this question already posted, so I will just add a caution. Be careful using mean and standard deviation on non-normally distributed data. Consider the values from a bi-modal distribution: -50, -32, -43, -47, +45, +53, +39, +35. Mean is zero (SD=46), yet none of the values are close to the mean. Another example is rolling one 6-sided die. I do this many times and calculate the average at 3.5, yet it is not possible to get a roll of 3.5. The mean is not the most likely outcome from another roll of the die.

Yes, the standard deviation can be greater than the mean and whether it is a good or a bad thing, depends on the sort of data being looked at (or investigated). It is not an abnormal. As a matter of fact, a standardized normal distribution data has a mean value of 0 and SD of 1. The better question would be "what is the implication of the standard deviation higher than the mean?"

There is a relationship between SD and mean. SD is calculated after subtracting the mean from each data in the data-sets and getting a standardized result (i.e. removing any negation). This tells you the standard distance each value should be from the mean (plus or minus). This distance is also a measure of how precise each data (or samples) in the are from themselves. Depending on the sort of data you have, if the standard deviation is higher than the mean, it may suggest any of the following:

1. Nothing. No significant meaning. Just numbers to quantify information.

2. There is no/poor precision amongst the sample or data set(s). This means there is a significant distance between the highest and lowest values.

3. There is an outlier amongst the data set. This might also imply random errors and can suggest you discard a particular sample/data or redo the analysis (the source of the data obtained).

4. You are out of statistical confidence (but this one depends on what we want as alpha).

5. Your data is skewed. You may need to normalize your data (or not, it depends on what you are doing).

6. There is a wide range of variation amongst the data/sample sets. The data set is not from the same source (As a good thing).

7. The standard deviation may not be the best tool to explain the variation of the data-sets. Look at the standard error of mean or the covariance.

8. The mean may not be the best measure of accuracy or central tendency. Look at the median or the mode.

How you make an interpretation of this fact really matters. As I have stated earlier, the implication of SD > mean depends on the sort of data being investigated. Your field, the type of data-set being analyzed and the purpose of your experiments/research should be considered. In some cases, you may want to normalize your data before further analysis. You may also have noticed that for larger data-sets, whenever your SD > mean, your null hypothesis usually fails at 95% CL (for inferential statistics).

I hope this is useful.

Standard Deviation measures variability between data sets and mean measures central tendency of data normality ..so the two cant be the same because the aim is different

Emeka Thompson Nwankwere was apt in his answers

It is not possible for SD to be greater than mean. However, when such observations are recorded then it does imply that something is fundamentally wrong with the data set and this calls for re-evaluation of where this error maybe coming from. However, I always recommend that standard error (SE) of the mean be used instead of SD as SE is a more reliable and precise index.

I agree with Oju Ibor.....it's not possible....

Yes, it is possible, sometimes when you have alot of 0 in you data set, I have experienced such in the past

Normally Mean is always greater than SD, but in some cases it does happen that the SD is greater than the mean, some time when u have zeros or the values in d data are far apart from one another

There are possibilities when dealing with negative numbers.

Yes. the SD could be greater than its mean. Consider the the absolute difference between the pre and post test which has negative values,

Yes. the SD could be greater than its mean.

Yes, it is possible. For example, taking measurements from different sources, which have extreme values such as 5, 30 and 200. The mean would be 78.33 and SD would be 86.62.

It is not uncommon to have SD greater than mean. It only tells you that the dataset is heterogeneous and uncorrelated which needs to be treated either by transforming it or by applying non parametric statistics to get a true picture of what is going on.

It is possible for SD to be greater than the mean, this is common in the case of Over-dispersed count data when the variance is greater than the mean, it is likely that that the SD will be greater than the mean in this case. This is an example from the summary statistics I just ran in excel.

Mean: 3.389192

Standard Error: 0.083919

Standard Deviation: 3.405692

Sample Variance: 11.59874

Kurtosis: 9.020266

Skewness: 2.611498

Range 26

Minimum: 1

Maximum: 27

Sum: 5582

Count: 1647

So, In am not in support of Oju Ibor and Andem Bassey Andem point of view.

Yes, SD can come out greater than the mean, when you have extreme variables or a mix of negative and positive values. But when this happens, it is a pointer to the nature of your data. If such occurrence defies logical explanation, then you need to recheck your datasets to address the error. SD just gives you a feeling of how dispersed your individual datum are to each other. the higher the SD, the greater the dispersion.

It is possible only in datasets with skewed distributions.

Yes

Standard deviation greater than the mean can happen even if the data are not skewed. Skew is a different descriptor of the shape of the distribution.

Positive and negative values are not relevant. This condition can happen for any mix of positive and negative values including all values being positive.

It can happen in real data without error. Real data can have extreme values. I sample a distribution and in my one sample of three values I happen to get one value that occurs once in 1000 observations. I could figure this out if I would take more samples but I only gathered three.

Correlation or the lack thereof has nothing to do with it.