Question

Instructions: Answer the questions below, NO PLAGIARISM.

*What are the strengths and limitations of the range?

*Can the measure central tendency and the measures of spread be used together to describe a set of scores? Of so, how?

*How are the standard deviation and the variance similar? how are they different?

*Create a question using standard deviation, including the answer.

Answer 1

1) Range - max(xi)- min(xi) , the only strengths of range is that it is easy to calculate and rigidly defined , the limitations of range include

1- it does not include all the observation in it's calculation , so it does not measure the spread in majority of values in your dataset

2 - affect of fluctuation in sampling is huge on range as it depends only on the extremes of the data set and extremes changes from sample to sample hence range

3) for open end intervals we cannot calculate the range

2 ) yes both can be used to describe the set of scores

The measure of central tendency is used to summarize the dataset by typically representing it with the central value , this central point represents the whole dataset

Now measure of the spread comments about your measure of central tendency such as mean , if your measure of spread is large it tells us that the measure of central tendency used maybe not the best for representing the dataset , the measure of spread basically tells us about the spread or variability in the dataset , so both measure of central tendency and measure of spread should work in conjunction with measurement of spread

3- both variance and standard deviation are measurements of spread , standard deviation is square root of variance

Standard deviation is expressed in the same unit of original dataset as opposed to the variance which is expressed as the squared units , unlike variance , standard deviation is much more intuitive and closer to the values of the original dataset

Question made using standard deviation

Given standard deviation of the random variable x = 3. Find it 'a variance

Ans - variance is square of standard deviation , so variance will be = 3x3 = 9

Variance =9