Module 2 - Section 3

Question 1

shifting data

Answer 1

adding or subtracting a constant to every data value

Question 2

what affect does shifting data have on center?

Answer 2

it will increase or decrease the value by the same constant it was shifted

Question 3

what affect does shifting data have on percentiles?

Answer 3

it will increase or decrease the value by the same constant it was shifted

Question 4

what affect does shifting data have on max/min?

Answer 4

it will increase or decrease the value by the same constant it was shifted

Question 5

what affect does shifting data have on range?

Answer 5

it will not change the value

Question 6

what affect does shifting data have on IQR?

Answer 6

it will not change the value

Question 7

what affect does shifting data have on standard deviation?

Answer 7

it will not change the value

Question 8

rescaling data

Answer 8

multiplying all the data values by a constant

Question 9

what measures of data change when we rescale data?

Answer 9

center, position, and spread are all multiplied by the constant
shape remains unchanged

Question 10

z-score

Answer 10

a measure of how many standard deviation away from the mean the measurement lies and in which direction
z = (y - μ) / 𝜎

Question 11

standardized value and some of its properties

Answer 11

the z score
shifts data by subtracting by the mean and rescales by dividing by the standard deviation
helps compare values of different scales with different units
shape stays the same
center becomes 0
spread (standard deviation) is 1

Question 12

what does a negative, positive and 0 z-score tell us

Answer 12

positive - above the mean
negative - below the mean
0 - is the mean

Question 13

density curve

Answer 13

a smooth curve that may fit the histogram
above or on the horizontal axis
area between curve and horizontal axis = 1

Question 14

How can we use density curve to solve problems

Answer 14

we can find the proportion of observations that fall in a range or P (a

Question 15

Normal distribution

Answer 15

bell shaped histograms
provides a reasonable estimation
very common

Question 16

properties of a normal distribution

Answer 16

symmetric, unimodal, bell-shaped
N(μ,𝜎) represents the normal model with a given mean and standard deviation
for every combination of μ and 𝜎 there is a different curve

Question 17

standardization of a normal curve

Answer 17

always has 𝜎 = 1 and μ = 0

or z ～ N(0,1)

Question 18

How can we check if a set of data is normal

Answer 18

• graph and see is shape is unimodal and symmetric

- make a histogram and a Normal probability plot or Q-Q plot aka quantile-quantile plot

Question 19

Q-Q plot

Answer 19

AKA Normal probability plot
graph to determine if a normal distribution plot is appropriate
straight line means normal
deviations from a straight line is not normal data

Question 20

The Empirical rule

Answer 20

68-95-99.7 rule
68% falls within 1𝜎 of μ
95% falls within 2𝜎 of μ
99.7% falls within 3𝜎 of μ
for normal distributions only

Question 21

when do we use z tables

Answer 21

has z-scores