Exam 4: Exploring Data: Variability

Data Set 4-6: -1, 3, 0, 2, 1 -Suppose the scores in Data Set 4-6 were ratings of five freshmen. A question arose about the standard deviation of the ratings of the entire class and these five were taken to be a representative sample. The standard deviation is

Suppose you had three numbers with a mean of 2. You calculated a deviation score for each of the three numbers and then added the deviation scores. The sum would be

For each set below circle the letter of the more variable group. -Set 1:

Which of the following is (are) not mathematically possible if only one distribution is being considered?

"Aha!" exclaimed Professor Sandy Sunshine, "the Registrar said this year's freshman class had lower SAT scores on average than last year's, but I declare, I have more brighter students than ever before." Suppose that the statement is true and that the Professor's students are representative of the whole class. Write an explanation of how this could be, using concepts in Chapter 4.

For a set of scores the sum of the deviation scores will be zero

The interquartile range tells you the scores that were made bypercent of the distribution.

Your text identifies three different standard deviations.

Find S using the definitional formula which has $\Sigma ( X - \bar { X } ) ^ { 2 }$ in the numerator. -Scores: 5, 4, 2, 1

The standard deviation of the IQ's of students at a high school for the gifted and talented is the standard deviation of the IQ's of students at a high school, that accepts everyone in its district.

A standard deviation equal to 0 is an impossible value.

Another name for $\Sigma$ ( $X$ - $\bar { X }$ )² is

Which of the following distributions is the least variable?

On some items grocery stores all charge the same price. On other items some stores charge less and some stores charge more. In shopping for bargains it makes sense to pay attention to the prices of items that vary a lot and to not pay much attention to the price if all stores charge the same. What quantitative method expresses this difference in items? Explain.

Data Set 4-1: 2, 7, 3, 6, 2 -For Data Set 4-1, the range is

You will get a negative number as a standard deviation

Finding the interquartile range first requires a calculation of percentiles.

Data Set 4-7: These are all the scores that exist for an entire group. 1, 0, 5, 6 -A raw score of 6 in Data Set 4-7 has a deviation score of

Find the range, IQR, and $\hat { S }$ X f 7 2 6 3 5 5 4 3 3 3 2

The formula for the standard deviation of a sample used to estimate ? has N -1 in the denominator.