If the value of the standard deviation exceeds half the value of the arithmetic mean, this means that the data is not homogeneous and data conversion must be done or the outliers should be treated. Is this correct?
Certainly, here's a rephrased version:
Indeed, the standard deviation can surpass the arithmetic mean value. In the realm of statistics, the standard deviation serves as a gauge of the extent of diversity or spread within a set of data points. It quantifies the degree to which the data deviates from the mean.
When data points exhibit significant dispersion, indicating a substantial amount of variability, the standard deviation tends to be comparatively larger than the mean. Under these circumstances, it's entirely plausible for the standard deviation to exceed the arithmetic mean.
To illustrate this concept, consider a straightforward example. Suppose you possess a dataset containing exam scores for a group of students:
Exam Scores: 60, 65, 70, 75, 80
To compute the mean: (60 + 65 + 70 + 75 + 80) / 5 = 70
Now, let's calculate the standard deviation. Without delving into the mathematical intricacies, the computed standard deviation is approximately 6.24.
In this particular example, the standard deviation (6.24) does, in fact, surpass the arithmetic mean (70). This implies that the scores exhibit some degree of deviation from the mean, signifying variability in the students' performance.
In summary, it's entirely typical for the standard deviation to be greater than the arithmetic mean value when data displays variation or dispersion. The standard deviation furnishes valuable insights into the extent of deviation among data points from the mean.
Hi
some points regarding your question
1)if your data are all negative, the mean is negative and the standard deviation is positive.
2) When standardizing data, the mean of the new standardized data will always be zero, but the standard deviation will be one.
3) If you subtract a positive constant from all data points, the mean of the new data will shift to the left, but the standard deviation will not change.
Finally, you may read the following post
https://stats.stackexchange.com/questions/30303/how-to-simulate-data-that-satisfy-specific-constraints-such-as-having-specific-m
Yours,
Hamid
Yes, the standard deviation can be higher than the arithmetic mean value, because SD measures how data deviates from the mean, thereby showing that the data is more spread out, but that does not mean that the data is less reliable.
Use of median with interquartile range could be used in this situation instead of mean with SD
Agree with previous answers. All are on the mark with this exception: homogeneity is not the issue. Possible to have a negative and positive SD that is larger than the mean typical of negative and positive skewed distributions. BTW those visually are opposite of what you would expect. Distribution hump on negative side is called positive and the reverse for the positive side of the distribution.
More than likely your distribution has a VERY wide range (read variation) AND your sample size is TOO small to pickup the ACTUAL variation needed for the SD to be sensitive enough to be more in alignment with statistical norms. Also, research the use of POWER and SAMPLE size to feel comfortable with your study.
Hope this is helpful.
IF SD>MEAN, THEN DEVIATION OF THE OBSERVATIONS HIGHER FROM MEAN. THERE WE CANNOT OBSERVE RHE UNIFORMITY AMONG OBSERVATIONS. IT SHOWS NEGATIVENESS OF THE DITRIBUTION.
Yes, it is possible for the standard deviation to be higher than the arithmetic mean. The standard deviation measures the dispersion or spread of data around the mean. If the data points are widely spread out, the standard deviation will be larger. On the other hand, the arithmetic mean represents the average value of the data points. It is possible for the data to have a high degree of variability, resulting in a large standard deviation, even if the mean is relatively small.
- Badges
- Science topic
- Similar topics
- Geoscience
- Asia
- India