Sum of squares of deviations from the mean is small.
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A small standard deviation indicates that the data points in a dataset are close to the mean or average value. This suggests that the data is less spread out and more consistent, with less variability among the values. A small standard deviation may indicate that the data points are clustered around the mean.
The measure commonly used to find the spread of marks in an examination is the standard deviation. It provides a numerical value that indicates how spread out the scores are from the mean score. A larger standard deviation suggests a wider spread of scores, while a smaller standard deviation indicates a more clustered distribution of scores.
Stanford-Binet intelligence scale results are measured by calculating the individual's intelligence quotient (IQ). This is done by comparing the person's performance on the test to the performance of others in the same age group. The IQ score is a standardized measure that represents a person's cognitive abilities compared to the general population.
Relative Standard Deviation (RSD) is a measure of precision (not accuracy). RSD is sometimes called coefficient of variation (CV) and often is calculated as a percentage. s = standard deviation x = mean RSD = s/x, as a percentage, (s/x) *100 The RSD allows standard deviations of different measurements to be compared more meaningfully. For example, if one is measuring the concentration of two compounds A and B and the result is 0.5 (+/-) 0.4 ng/mL for compound A and 10 (+/-) 2 ng/mL for compound B, one may look at the standard deviation for compound A and say because it is lower (0.4 vs. 2) than for B, the measurement for A was more precise. Actually this is not the case. When the %RSD is used the new values for compound A and B are 0.5 (+/-) 80% and 10 (+/-) 20% respectively, therefore, the measurement for compound B is more precise.
The formula to calculate the z-score of a data point is: ( z = \frac{(x - \mu)}{\sigma} ), where (x) is the data point, (\mu) is the mean of the data set, and (\sigma) is the standard deviation. For example, if you have a data point of 85, a mean of 75, and a standard deviation of 5, the z-score would be ( z = \frac{(85 - 75)}{5} = 2 ). This means the data point is 2 standard deviations above the mean.
If the minimum value is the minimum observed value then it indicates that the distribution goes below the minimum observed value.If the minimum value is the minimum defined for the distribution then it indicates thatthe data do not come from the proposed distribution,estimates for the mean or standard deviation are incorrect, oryou have got a sample which is atypical.