SB 3.3-3.4 (plus 3.2 Empirical Rule)

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

give unreliable descriptions of the distribution.

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

the interquartile range

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% Reason: 38 and 62 are one standard deviation away from the mean → [μ ± σ]

For a normally distributed population, what percentage of measurements are within plus or minus two standard deviations of the mean?

95.44%

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

-2 Reason: Q1 - 1.5(IQR) = 12 - 1.5(8) = 0, so 1 is not an outlier.Q3 + 1.5(IQR) = 20 + 1.5(8) = 32, so 30 and 31 aren't either.

For a normally distributed population, 68.26% of measurements are within plus or minus ___________ standard deviations of the mean.

1

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

1 and 17 Reason: Q1 - 1.5(IQR) = 7 - 1.5(4)= 1 Q3 + 1.5(IQR) = 11 + 1.5(4) = 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

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

13 Reason: i = 0.80(8)8 = 6.4 Since the index is not an integer, we round up to the 7th measurement, giving 13

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

15%

Match the following quartiles to their equivalent statistics:

1st Quartile: 25th Percentile 2nd Quartile: Median 3rd Quartile: 75th Percentile

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 Reason: __ This is x ± 3s which holds for approximately 99% of customers.

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

6

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

6 i=0.80(8)=6.4

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

68

Identify the type of graphical model shown:

A box-and-whiskers display

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 Reason: IQR = Q3 - Q1

Suppose the least squares line relating sales y of an item to its price x is ŷ = 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.

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.

The empirical rule tends to give unreliable estimations when for populations that are: (Select all that apply)

Negatively skewed Positively skewed

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

Q1; the smallest measurement that is not outlying.

Which measure of central tendency is the same as the second quartile?

The median

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

Looking at the provided box-and-whiskers display, we can conclude that the population is probably ______.

positively skewed

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. r=Sxy/SxSy