SB 3.3-3.4 (includes empirical rule)

A set of measurements is divided into four parts, each containing approximately 25% of the measurements. These three dividers are called

quartiles

Which of the following are true statements about the sample correlation coefficient r?

-r takes values between -1 and 1. -If r is near 0, there is little to no linear association between x and y.

For a normally distributed population, 68.26% of measurements are within plus or minus _____ standard deviation(s) of the mean.

1

Calculate the 80th percentile for the following measurements: 3, 5, 7, 8, 9, 11, 13, 15

13

On which population distributions can the empirical rule be used?

- Mound-shaped distributions showing not much skew in either direction -Normal distributions

A data set has Q1 = 12 and Q3 = 20. Which measurements in the set { -2, 1, 30, 31} would be considered outliers?

-2

The empirical rule tends to give unreliable estimations when for populations that are:

-Positively Skewed -Negatively Skewed

The length of the interval that contains the middle 50% of measurements is known as ______.

the interquartile range

Sam's exam score was good but 32% of students scored higher than Sam. That places Sam in the _______ percentile.

68th

Suppose the least squares line relating sales y of an item to its price x is ŷŷ = 65.2 - 5.1x. Which of the following are true statements?

-For every one unit increase in price, we expect sales to decrease by 5.1 units. -Sales tend to increase as price decreases.

A data set has Q1 = 7 and Q3 = 11. Determine the lower and upper limits for a box plot.

1 and 17

Arrange the steps (from first to last) to create a box-and-whiskers display.

1. Calculate Q1, Md, and Q3 2. Draw a box that extends from Q1 to Q3. Draw a vertical line through the box at Md. 3. Mark the values of the lower and upper limits. 4. Draw the whiskers. 5. Plot the outliers.

Pat's exam score placed Pat in the 85th percentile. This means that _____% of students scored higher than Pat.

15

A sample of 100 bank customer waiting times revealed that xx = 8 minutes and s = 2 minutes. Assuming that the population is normally distributed, the empirical rule states that almost all customers will have to wait between ______ and _____ minutes.

2 and 14

Calculate the 25th percentile for the following measurements: 3, 5, 7, 8, 9, 11, 13, 15

6

A population has a mean of 50 and a standard deviation of 12. According to the empirical rule, approximately what percentage of the population data are contained between 38 and 62?

68%

Match the (x, y) pairs below with the most reasonable estimate of their correlation coefficient. (A) x = height of husband; y = height of wife (B) x = height of person; y = length of right arm (C) x = time spent studying for a quiz; y = number of points missed (D) x = height of person; y = score on history quiz

A - 0.5 B - 0.95 C - (-0.6) D - 0

The interquartile range is the difference between which two quartiles?

First and third

For populations that are positively or negatively skewed, the empirical rule tends to ______.

Give unreliable descriptions of the distribution.

Suppose the slope of a least squares line is 2.5. If x increases by 2, how do we anticipate y will change?

It should increase by approximately 5.

In a box-and-whiskers display, the lower whisker is drawn from ____ to _____.

Q1; the smallest measurement that is not outlying.

True or false: A box-and-whiskers display is a visual representation of the Five Number Summary.

True

A ______ is a graphical summary of a data set's quartiles and interquartile range.

box-and-whiskers display