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Hint

1

percentile

the *p*th percentile of a distribution is the value with *p*% of observations are **less than or equal to it**

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2

standardized test statistic

AKA z-scores

measures how many standard deviations a data value is above (positive z-score) or below (negative z-score) the mean

has no units

the further from zero it is, the more unusual it is

a z-score of __+__2 is the boundary for an outlier

a z-score of __+__3 is the boundary for an extreme outlier

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3

z-score formula

(statistic - parameter)/standard deviation

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4

What does shifting data by adding or subtracting the same number from each observation affect?

mean

median

quartiles

min/max

five-number summary

percentiles

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5

What does shifting data by adding or subtracting the same number from each observation **not **affect?

standard deviation

range

IQR

shape

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6

What does shifting data by multiplying or dividing the same positive number from each observation affect?

all measures of center and spread

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7

What does shifting data by multiplying or dividing the same positive number from each observation **not** affect?

shape (may just be more spread out, but remains mostly the same)

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8

density curves

on or above horizontal axis

has an area of **exactly 1** underneath the curve

the mean is the point where the curve would balance if made of solid material

the median is the equal-areas point, where the area under the curve is divided in half

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9

What is the shape of the normal distrbution?

symmetric, single-peaked, and bell shaped

free of skew and outliers

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10

How is the center of a normal curve measured?

The mean (ÎŒ) is located at the midpoint and is the same as the median

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11

How is the variability of the normal curve measured?

standard deviation (Ï) measures the variability, or width

more spread = larger Ï and more variability, less spread = smaller Ï and less variability

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12

How are normal distributions named?

N (ÎŒ,Ï)

N (xÌ, Sx)

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13

About how much of the data falls within 1 standard deviation of the mean in a normal model?

68%

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14

About how much of the data falls within 2 standard deviations of the mean in a normal model?

95%

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15

About how much of the data falls within 3 standard deviations of the mean in a normal model?

99.7%

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16

The normal model is ________, so we never say 0% or 100%

infinite

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17

How do you find the percentage when z-score is not exactly 1, 2, or 3?

â2ndâ > âvarsâ > ânormalcdfâ

input the z-score of the lower boundary and the z-score of the upper boundary, then hit âPasteâ and then âenterâ

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18

How do you find the z-score if you just have the percentile?

â2ndâ > âvarsâ > âinvnormâ

input the percentile as a decimal into âareaâ and choose whether the area is to the left, right, or in the center

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19

Two ways to determine if the normal model is appropriate

Histogram appears unimodal and symmetrical (free of skew and outliers)

Double check by constructing a **normal probability plot** that should appear roughly linear

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20

How to construct a normal probability plot

Input your data into L1

then â2ndâ > ây=â

go to âPlot 1â turn on normal probability plot, then hit âzoomâ > â9â

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