Question

Discuss the advantages and disadvantages of standard deviation

Answer 1

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 items in the series. So, it is the best measure of dispersion.

3. Less Affected: -

Standard deviation is least affected by the sampling fluctuations than other measures (mean deviation and quartile deviation).

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.

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.

Answer 2

Answer:

Standard deviation is complex to compute and difficult to understand as compared to other measures of dispersion. Standard deviation is based on all the items in the series. So, it is the best measure of dispersion.

Step-by-step explanation:

• Standard Deviation: In the year 1893, Karl Pearson first proposed the idea. Since it lacks the flaws and restrictions that other measures of deviation possess, it is the most often used measure of dispersion. The square root of the mean of the squared deviations subtracted from the arithmetic mean can be used to define it. A other name for it is the root mean square deviation. The standard deviation is represented by the Greek letter "s," which is pronounced "sigma."

Standard Deviation characteristics. Standard deviation characteristics need to be highlighted. As follows:

• Dispersion or variability must be larger the higher the standard deviation. In other words, a lower standard deviation indicates greater data homogeneity, and the opposite is also true.
• The distribution with the smaller standard deviation has a more representative mean when two distributions have the same mean.

Standard Deviation Benefits

1. Considering all factors: All of a series' data are used to calculate the standard deviation. No worth is disregarded.
2. Reliable Metric: The standard deviation is a reliable metric for gauging dispersion. As a result, it is applicable in every circumstance.
3. Minimal Impact of Sampling: The Standard Deviation is not significantly affected by changes in sampling. This is so because a sample's overall values serve as the basis for deviation.
4. Standard Deviation is amenable to further algebraic treatment.

Standard deviation drawbacks:

1. Difficult: Calculating and comprehending standard deviation are challenging tasks.
2. Greater weight given to extreme values: Extreme values are given more weight when calculating standard deviation.
3. The following are some ways in which Mean Deviation and Standard Deviation differ from one another despite the fact that both of them are based on all the items in a distribution:

• Algebraic signs are disregarded when computing the mean deviation. However, they are taken into account when determining the standard deviation.
• The mean deviation is computed using the median or mean. However, the standard deviation is only calculated using the mean.