Why do we need to study the variation of a collection of data? Why isn’t the ave

Question

Why do we need to study the variation of a collection of data? Why isn’t the average itself adequate? What makes the standard deviation more valuable as a measure of variation than the easier to compute range?

Consider robin’s eggs; the mean weight of a collection of robin eggs is 0.72 ounce and the standard deviation is 0.12 ounce. Now consider elephants; the men weight of elephants in the zoo is 6.42 tons, with a standard deviation of 1.07 tons. The units of measurement are different and there is a great deal of difference between the weight of an elephant and that of a robin’s egg. Yet, the coefficient of variation is about the same for both. Comment on this.

Post additional related questions for the class.

Explanation / Answer

Why do we need to study the variation of a collection of data?

because the standard deviation of both data come from different proportions, sample and population

Why isn’t the average itself adequate?

Because the units of measurement are different so we need to use a better parameter where the units does not matter

What makes the standard deviation more valuable as a measure of variation than the easier to compute range?

the standard deviation is more valueable because we use all the data

when the range only use the max and min data

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.