3.3 z-scores and boxplot

Question 1

z-score equation

Answer 1

(x-“mu” or population mean)/sigma or standard deviation

Question 2

z-score can be negative or positive

Answer 2

negative means below mean and positive means above mean

Question 3

use the empirical rule to interpret z-scores with bell-shaped populations

Answer 3

because z-score is the number of standard deviations from the mean

Question 4

z-score and the empirical rule

Answer 4

z= -1/1 is 68% z=-2/2 is 95% z=-3/3 is almost all

Question 5

find the value x with a given z-score (answer is n 3 decimal places)

Answer 5

x=”mu”+zsigma (use GEMS so zsigma goes first)

Question 6

outliers

Answer 6

the value that is considerably larger or considerably smaller than most of the values in a data set

Question 7

interquartile range

Answer 7

a measuring method to detect outliers. Is Q3-Q1

Question 8

interquartile range equation

Answer 8

IQR=Q3-Q1 (subtracting the first quartile from the third quartile)

Question 9

IQR method

Answer 9

most frequent method used to detect outliers.

Question 10

Steps for IQR method

Answer 10

1. find the first quartile Q1 and third quartile Q3. 2. Compute the interquartile range: IQR-Q3-Q1. 3. Compute the outlier boundaries. These boundaries are the cutoff point for determining outliers

Question 11

Lower Outlier Boundary

Answer 11

Q1-1.5(IQR)

Question 12

Upper Outlier Boundary

Answer 12

Q3+1.5(IQR)

Question 13

Finding Interquartile Range from the calculator

Answer 13

Using the 1-Vars States menu you can find Q3 and Q1, then subtract to find what the range is. Then put them in the lower and upper outlier boundary. Any number above or below is an outlier.

Question 14

boxplots

Answer 14

can determine skewness in a data set. outliers are plotted seperately using x’s.

Question 15

The boxes are the Q1, median and Q3

Answer 15

The whiskers are the smallest and largest data set within the lower and upper and lower outlier boundaries

Question 16

Plotting Boxplots in the calculator

Answer 16

Enter data in L1, press 2nd, Y= then select the boxplot. You might have to press 1 to access the Plot1

Question 17

If the median is closer to the first quartile than the third quartile/ if the upper whiskey is longer

Answer 17

the data is skewed to the right

Question 18

if the median is closer to the third quartile than the first quartile, or the lower whisker is longer than the upper

Answer 18

the data are skewed to the left

Question 19

if the median is about halfway and the whiskers are equal in length

Answer 19

the data are about symmetric