QUIZ 2-Ch. 2 (1/30)

Question 1

3 measures of central location:

Answer 1

mean, median, mode

Question 2

calculating mean/average:

Answer 2

sum/count

Question 3

X̄

Answer 3

“x-bar” represents the mean of a variable

(usually a mean of a sample)

Question 4

weighted mean definition:

Answer 4

not all values contribute equally

useful when data is displayed in a frequency table

think: hw, tests, quizzes all worth different amounts of your overall grade in class

Question 5

μ

Answer 5

“mu” represents the population mean

Question 6

mean definition:

Answer 6

the balance point for a set of data

most commonly used measure of central location

all values used in calculation

Question 7

mean is affected by:

Answer 7

extreme values (causes skewed distribution)

it gets pulled in the direction of the skew

Question 8

median definition:

Answer 8

midpoint of a set of data

not all values used in its calculation

Question 9

how to find a median:

Answer 9

1. order the data
2. position= (n+1)/2

Question 10

median is NOT affected by:

Answer 10

extreme values

Question 11

calculation property of a mean:

Answer 11

Σ(Xi-x̄)=0

will always equal 0!

think: when calculating variance third column (x-x̄) all of those values have to sum up to 0!

Question 12

mode definition:

Answer 12

the value (s) that occurs most frequently

it’s the only numerical summary that is useful for qualitative data

Question 13

when skewed right:

Answer 13

mode<median<mean

Question 14

when skewed left:

Answer 14

mean<median<mode

Question 15

3 measures of dispersion (variation):

Answer 15

range, variance, standard deviation

Question 16

range definition:

Answer 16

max-min

weak measure because only looks at the two values on the end

Question 17

variance definition:

Answer 17

reflects the dispersion of all the values around the mean of the data

it is in squared units of measurement

Question 18

sample variance calculation:

Answer 18

s^2=Σ(Xi-x̄)^2/(n-1)

when calculating variance table: last column (take sum & divide by n-1)

Question 19

Empirical Rule: x̄ ±1s

1s= 1 standard deviation

Answer 19

approx. 68% of the observations will lie with x̄ ±1s

Question 20

Empirical Rule: x̄ ± 2s

2s= 2 standard deviations

Answer 20

approx. 95% of the observation will lie with x̄ ± 2s

Question 21

Empirical Rule: x̄ ± 3s

3s= 3 standard deviations

Answer 21

approx. 99.7% of the observations will lie with x̄ ± 3s

Question 22

Chebyshev’s Theorem:

Answer 22

the proportion of observations in any sample that lie within “k” standard deviation of the mean is at least 1-1/(k^2) for k>1

Question 23

percentiles definition:

Answer 23

% of the data less than or equal to a value

think: SAT if you were in the 80th percentile

Question 24

Q1

first quartile

Answer 24

25% of the data ≤ Q1

Question 25

Q2

second quartile

Answer 25

75% of the data ≤ Q3

Question 26

IQR definition:

Interquartile Range

Answer 26

spread of the “middle 50%” of the data

*IQR=Q3-Q1