STAT MOD 2: Chapter 3

Question 1

What is the measure of center?

Answer 1

where the data distribution is located along the number line

provides information about what is TYPICAL

Question 2

What is the appropriate measure of center if distribution is symmetric?

Answer 2

mean/average = symmetric

Question 3

What is the appropriate measure of center if distribution is skewed?

Answer 3

median = skewed or has outliers

Question 4

What is measure of spread?

Answer 4

how much variability is in a data distribution

provides information about how much individual values tend to DIFFER from one another

Question 5

What is the appropriate measure of spread if distribution is symmetric?

Answer 5

standard deviation = symmetric

if applicable, use empirical rule

Question 6

What is the appropriate measure of spread if distribution is skewed?

Answer 6

Interquartile range = skewed or has outliers

Question 7

What is notation (n)?

Answer 7

the number of observations in the data set

Question 8

What is mean? How do you compute mean?

Answer 8

numerical average

Excel command: =AVERAGE(dataset)

Add up all values then divide by number of values

Hint: might be a list of numbers or stem-and-leaf plot, dotplot display

Question 9

What is the median? How do you compute the median?

Answer 9

Middle data value for an odd number of observations or average of two middle values for an even

Excel command: =MEDIAN(dataset)

Order the values, find middle value or average of middle lines

Question 10

Is the mean resistant to outliers?

Answer 10

No, mean is a non-resistant measure

Outliers affect mean because the mean takes into account all of the values and pulls the mean towards it

Question 11

Is the median resistant to outliers?

Answer 11

Yes, median is a resistant measure

Outliers do not affect mean as it’s just the middle value

Question 12

What is the mean/median on the histogram?

Answer 12

Mean: the point where the histogram would balance

Median: the point where half the area falls to the left and half to the right (SPLITS in the middle)

Question 13

Where does mean/median fall relative to one another in a SYMMETRIC distribution?

Answer 13

mean and median are both in the middle or approximately the same

Question 14

Where does mean/median fall relative to one another in a RIGHT SKEWED distribution?

Answer 14

mean > median (more to the right than median)

Question 15

Where does mean/median fall relative to one another in a LEFT SKEWED distribution?

Answer 15

mean < median (more to the left than median)

Question 16

How do you compute range?

Answer 16

Range = maximum - minimum

Question 17

What is interquartile range? How do you compute interquartile range?

Answer 17

How spread out the middle half of the data is

IQR = Q3 - Q1

Question 18

How do you find third quartile?

Answer 18

Taking median of upper half of the ordered data values (all numbers larger than median of dataset)

Question 19

How do you find first quartile of the data set?

Answer 19

Taking median of lower half of the ordered data values (all numbers smaller than median of dataset)

Question 20

What is standard deviation?

Answer 20

Roughly the average distance from the mean (how many units away from the mean)

Question 21

What is the sample standard deviation?

Answer 21

How far away on average are the observations from the mean

• if given several datasets, know which has largest or smallest standard deviations

Question 22

What kind of data sets would have larger standard deviations?

Answer 22

Data sets with bigger spreads or more spread/variability have higher standard deviation

Question 23

Notation for mean of population and sample?

Answer 23

µ - mean of population
x bar - mean of sample

Question 24

Notation for standard deviation of population and sample?

Answer 24

sigma - population
s - sample

Question 25

What are resistant/robust measures?

Answer 25

Median (center) Interquartile Range (spread)

Question 26

What are non-resistant/robust measures?

Answer 26

Mean (center) Standard deviation (spread) - Range - Correlation

Question 27

How do you construct a box plot?

Answer 27

Boxplot: visual display for five-number summary (MIN, Q1, MEDIAN, Q3, MAX) 1) Label axis (whiskers) with the minimum and maximum of data - if min/max are outliers, use asterisk and use the next largest/smallest value as endpoint 2) Draw box with lower end at Q1 and upper end at Q3 3) Draw a line through the box at median

Question 28

What is an outlier?

Answer 28

A value that falls more than 1.5 IQR below QI or more than 1.5

Question 29

How do you determine if a value is an outlier?

Answer 29

Use fences method - first find Q1, Q3, and IQR Lower fence = Q1 - 1.5(IQR) - if number falls below the computed value, outlier Upper fence = Q3 + 1.5(IQR) - if number falls above the computed value, outlier

Question 30

What elements do you have to know about comparative box plots to compare distribution of a variable for different groups?

Answer 30

X indicates mean, line indicates median - know whether box plots are symmetric, right skewed, left skewed - know which box plot has bigger/smaller range, high IQR, larger center, spread

Question 31

What is the empirical rule?

Answer 31

68-95-99.7 rule - 68% fall within 1 standard deviation of mean - 95% within 2 standard deviations of mean - 99.7% fall within 3 standard deviations of mean

Question 32

What is normal distribution?

Answer 32

A bell-shaped curve with many data points in the middle and few out in the tails

Question 33

What is a z-score?

Answer 33

Measure how far an observation is from the mean in standard units (standardizing the observations) x - mean/standard deviation

Question 34

What is the percentile?

Answer 34

A number r between 0 and 100, the rth percentile is a value such that r percent of observations fall at or below that value Ex: 20th percentile means at least 20% of data fall at or below that value and 80% of data fall at or above that value