Question

i) Once you have calculated a standard deviation, discuss its meaning.?

ii) Discuss the pros and cons of the using the variance and the standard deviation in their usefulness in data interpretation.

Answer 1

(i) We calculate standard deviation to measure the dispersion of the data. By dispersion, we mean that how the data scatter or spread over the space . More specifically we measure the distance of each data from the central value or the mean value to figure out the spreadness of the data.

(ii)  

Advantages/Merits Of Standard Deviation

1. Rigidly Defined

Standard deviation is rigidly defined measure and its value is always fixed.

2. Best Measure

Standard deviation is based on all the values in the data. So, it is the best measure of dispersion.

3. Less Affected

Standard deviation is least affected by the sampling fluctuations than other measures.

4. Suitable For Algebraic Operation

Standard deviation can be used for mathematical operations and algebraic treatments. It is also applicable in statistical analysis.

Disadvantages/Demerits Of Standard Deviation

1. Complex Method

Standard deviation is complex to compute and difficult to understand as compared to other measures of dispersion(range).

2. High Effect

Standard deviation is highly affected by the extreme values in the series.

3. Standard deviation cannot be obtained for open end class frequency distribution.

Usefulness  of standard deviation in data interpretation

we can compare the consistency of performance or any other kind of comparison among different sets of data using CV (coefficient of variation). In the formula of CV , we use standard deviation as follows

  CV = (mean / standard deviation) × 100 %