Chapter 3: Numerical descriptions of data

Question 1

mode

Answer 1

-most frequently appearing value, or common frequency class
- “humps in distribution”
- need not be all the same height or count
-mostly to recognize bi-modal or multi-modal

Question 2

multi-modal

Answer 2

-often a tip-off that different types of individuals in the data set

Question 3

mean or average

Answer 3

-useful when the data is roughly symmetrical and without many outliers
-can be misleading on very skewed data

Question 4

median

Answer 4

• the halfway point, roughly half are smaller than this value and half are larger
  -the measure of center is more resistant to skewness or outliers
  -frequently used for distributions like income or house cost
  -the value that lies in the middle of the data when the data set is ordered

Question 5

median with odd number of entries

Answer 5

-median is the middle data entry

Question 6

median with even number of entries

Answer 6

median is the mean of the two middle data entries

Question 7

advantage of using the mean

Answer 7

-the mean is a reliable measure because it takes into account every entry of a data set

Question 8

disadvantage of using the mean

Answer 8

-greatly affected by outliers
-if your data is skewed, then the mean is not the best way to measure the data- median is the best it is not effected by outliers

Question 9

Range

Answer 9

• just maximum and minimum, easier to find by sorting data
  -sensitive to outliers
  -most common

Question 10

Interquartile Range IQR

Answer 10

-range of middle half
-less sensitive to outliers
-the difference between the third and first quartiles
IQR = Q3-Q1
-Q1-1.5IQR (“Low Fence”)
-Q3 + 1.5IQR (“High
Fence”)

Question 11

standard deviation

Answer 11

-appropriate for symmetric distributions where the mean is a good measure of center
-tells you “on average” how much EACH data value differs (varies) from the mean
-The greater the STANDARD DEVIATION the greater the SPREAD of data

Question 12

canonical examples of variation

Answer 12

1. the weights of ping pong balls: (b/c of standards and high quality manufacturing, very little spread)
2. the weights of apples in a grocery store: some but no extreme variability
3. your little brothers rock collection: a lot of variation

Question 13

standard score (z-score)

Answer 13

-represents the number of standard deviations a given value x falls from the mean u

Question 14

percentile

Answer 14

-ranks by 100ths

Question 15

decile

Answer 15

-ranks by 10ths

Question 16

quartile

Answer 16

-ranks by 4ths

Question 17

quintiles

Answer 17

rank by 5ths

Question 18

percentile

Answer 18

the kth percentile is the data value that has k% of the data at or below that value

Question 19

Box and whisker plot

Answer 19

-exploratory data analysis tool
-highlight important features of a data set
- requires: minimum entry, first quartile, median, third quartile, maximum entry
-used to gage symmetry and spread of distribution
-multiple plots are convenient to compare two distributions

Question 20

mean = median

Answer 20

“normal symmetric distribution”
-no outliers on both ends that out weigh one another

Question 21

mean<median

Answer 21

(skewed left- small value outlier)
(think: skewed Left then the mean is Less than median)

Question 22

mean>median

Answer 22

(Skewed Right – large value outlier)

Question 23

Measures of variation are

Answer 23

1. range
2. deviation
3. variance
4. standard deviation

Question 24

Measures of Center are

Answer 24

1. mean
2. median
3. mode

Question 25

deviation

Answer 25

-is the difference between that particular value and the mean -the sum of deviation will always equal to zero

Question 26

variance

Answer 26

the SUM (∑) of the SQUARED DEVIATIONS divided by the TOTAL FREQUENCY.

Question 27

empirical rule

Answer 27

-can only apply this rule for normal data -(68 – 95 – 99.7 Rule)