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# Sta301 Graded Discussion Board Opening Date 03-02-2015 .... closing date 04-02-2015

Sta301 Graded Discussion Board Opening Date 03-02-2015 .... closing date 04-02-2015

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Why range is not considered as a good measure of variability? Why standard deviation is preferred over the other measures?”
Note: Discussion should be relevant. Irrelevant and unnecessary lengthy materials will not be considered. Also it is strictly informed that comments will not be received through emails

plz discuss here

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### Replies to This Discussion

Dear Students,

Graded Discussion Board for STA301 will be opened on February, 03, 2015 and will be remained open till February 04, 2015. The topic of this GDB will be,

“Why range is not considered as a good measure of variability? Why standard deviation is preferred over the other measures?”
Note: Discussion should be relevant. Irrelevant and unnecessary lengthy materials will not be considered. Also it is strictly informed that comments will not be received through emails. plz discuss here

Our main purpose here discussion not just Solution

We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.

there are three measure of variability range, inter quartile range and standard deviation. now what is that reason that standart deviation is more preferable among these three mothods

The Range

The range is the difference between the largest and smallest values in a set of values.

For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. For this set of numbers, the range would be 11 - 1 or 10.

Comparing the range,and standard deviation As the range is much less sensitive to changes in the data than the standard deviation. If a single value changes then the standard deviation, by definition, will also change. Hence the standard deviation is a more powerful summary measure as it makes more comprehensive use of the entire dataset. However,situations when the mean might not be an appropriate measure of centre were discussed previously. If the mean is not a meaningful summary of the centre of the data, then it follows that the standard deviation, which is calculated from distances around the mean, will not be a useful summary of the spread of the values. Therefore, if distributional assumptions (data is symmetric) can be made and there are adequate numbers in the sample to check those assumptions (as a rule of thumb it is often said that a sample size of at least 20 would be adequate), then the mean and standard deviation should be used to quantify the centre and spread of the measurements. Alternatively, if the data distribution is skew and/or the sample size is small then it is preferable to use the median and interquartile range to summarise the measurements

Among all measures of dispersion Standard Deviation is considered superior because it possesses almost all the requisite characteristics of a good measure of dispersion. It has the following merits:

1) It is rigidly defined.

2) It is based on all the observations of the series and hence it is representative.

3) It is amenable to further algebraic treatment.

4) It is least affected by fluctuations of sampling.

## Merits and Demerits of Range

A good measure of dispersion should be rigidly defined easily calculated, readily understood, should be capable of further mathematical treatment and should not be much affected by fluctuations of sampling.

Out of these the only merit possessed by Range is that it is easily calculated and readily understood.

As against this the Range as a measure of dispersion has the following demerits:

(i)      It is affected greatly by fluctuation of sampling.

Its value is never stable and it varies from sample to sample. In a class-where normally the heights of students range from 160 to 180 centimeters if a dwarf whose height is 100 centimeters is admitted, the range would shoot up from 20 to 80 centimeters. Thus* a single variation in the value of an extreme item affects the value of the range.

(ii)     It is not based on all the observations of the series:

If the heights of the shortest and tallest students remain unchanged and if the heights of all other students are changed, range would remain unaffected. Thus range does not take into account the composition of a series or the distribution of items within the extremes. The range of a symmetrical and an asymmetrical distribution can be identical. Two such distributions can never have the same dispersion.

(i)     It cannot be used in case of open-end distributions :

In open end distributions the lower limit of the lowest class and the upper limit of the highest class are not known.

very much simple GDB.....

We just need to write the demerits of Range and merits of standard deviation over range.

Just mix it up and ur recipe of GDB is prepared  demerits of Range and Merits of Standard deviation are mentioned Above....

Write all those points in ur own words.. dont try to copy the paragraph..   Kia hua D sis o.O   Confusion Range is the the difference between the largest and smallest values in a set of data. The Standard Deviation is a measure of how far the data points are spread out. One SD above and below the average represents about 68% of the data points (in a normal distribution).

There is not a direct relationship between range and standard deviation. But because both are measures of spread, the range can help (depending on the data) to draw conclusions about the SD.

An example is:
45, 45, 45, 45, 45
In this case, the Range is 0. Since they're all the same values, there is no deviation, so the SD is also 0.

If the data set were: 43, 44, 45, 46, 47, the range here is 4. You can see the data is more spread out than the first example, so the SD will be larger than 0 (in this case, it's about 1.6)

If the data set were 41, 43, 45, 47, 49, here the range is 8. This set of data is even more spread out; the SD is 3.2.

However, range is not tied to the SD. If the data set were: 41, 45, 45, 45, 49, the range is still 8, but the distribution is less spread out, so the SD would be less than 3.2; it's in fact 2.8.

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