Question

1. a. What are the disadvantages of each of the following measures of spread or variability? Range, Standard Deviation, Variance.

b. What are the advantages of each of the following measures of spread or variability? Range, Standard Deviation, Variance.

2. . Discuss when is it most appropriate to use each of the following probability models: Binomial, Poisson, Negative Binomial.

Answer 1

## 1. a. What are the disadvantages of each of the following measures of spread or variability? Range, Standard Deviation, Variance.

answer : for Range :

1)Relies on extreme values so if their are outliers in the data the range may give a distored picture of the variability .

2) it does not measure the spread of the majority of values in a data set .

3) it only measures the spread between highest and lowest values . As a result , other measures are required in order to give a better picture of the data spread .

## Standard deviation :

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

2) it is highly affected by the extreme values in the series .

3) it cannot be obtained for open end class frequency distribution .

## for variance :

1) one drawback to variance that it gives added weight to outliers ,

the numbers that are far from the mean . squaring these numbers can skew the data variance can be negative

2) It is not easy to interpret .

# b. What are the advantages of each of the following measures of spread or variability? Range, Standard Deviation, Variance.

Answer :

## for range :

1) it is easy to compute

2) it can be used as measure of variability where precision is not required .

## for standard deviation :

1) it is rigidly defined measure and its value is always fixed .

2) it is based on all the items in the series So it is the best measure of dispersion

3) it is least affected by the sampling fluctuations than other measures .

## for variance :

1) it treats all deviations from the mean the same regardless of their direction .

2) The squared deviations cannot sum to zero and give the appearance of no variability at all in the data

2. . Discuss when is it most appropriate to use each of the following probability models: Binomial, Poisson, Negative Binomial.

for Binomial :

it is used when there are two possible outcomes ( ex success and failure , pass and fail ..

for the fixed n size .

for Possion :

it is used to describe the distribution of rare events in large population for example at any particular time , there is a certain probability that a particular cell within a large population of cells will acquire a mutation acquisition is a rare event.

another example : number of accidents on high way when we exact no how many die .

for negative binomial :

this is used with discrete random variables this type of distribution concerns the number of trials that must occur in order to have a predetermined number of successes

that is number failures before getting the first success .