AP Unit 1-Exploring One Variable Data Vocabulary

Variable

a characteristic that changes from one individual to another

categorical variable

takes on values that are category names or group labels

quantitative variable

one that takes on numerical values for a measured or counted quantity

How to represent categorical data?

use frequency or relative frequency tables

Frequency table

gives the number of cases falling into each category

relative frequency table

gives the proportion of cases falling into each category.

Describe categorical data represented in frequency or relative tables.

Percentages, relative frequencies, and rates all provide the same information as proportions.

What can represent categorical data graphically

Bar charts, bar graphs

Classify types of quantitative variables

A discrete variable and a continuous variable can take on a countable number of values. The number of values may be finite or countably infinite, as with the counting numbers.

discrete variable

can take on a countable number of values. The number of values may be finite or countably infinite, as with the counting numbers.

continuous variable

can take on infinitely many values, but those values cannot be counted. No matter how small the interval between two values of a continuous variable, it is always possible to determine another value between them.

What Represent quantitative data graphically?

histograms, stem and leaf plot, dot-lot

Describe the characteristics of quantitative data distributions.

shape, center, and variability (spread), outliers, gaps, clusters, or multiple peaks.

unimodal

one main peak

bimodal

two peaks

Statisitcs

a numerical summary of sample data

What are the three common measures of variability or spread in a distribution?

range, interquartile range, and standard deviation.

How to find IQR

Q3-Q1

What is s^2?

sample variance

What are two ways to find outliers?

Q1-1.5(IQR)

Q3+1.5(IQR)

An outlier is a value located 2 or more standard deviations above, or below, the mean.

Why are the mean, standard deviation, and range considered nonresistant?

they are influenced by outliers

Why are the median and IQR are considered resistant?

outliers do not greatly (if at all) affect their value

What do the outliers affect?

the mean, standard deviation, and range

What do the outliers not affect the values?

median and IQR

What is the five number summary?

minimum, Q1, median, Q3, maximum

If the distribution is relatively symmetric, then the mean and median are what?

close to each other

If a distribution is skewed right, then the mean is usually what?

to the right of the median.

If the distribution is skewed left, then the mean is usually to the what?

the left of the median.

What can be used to compare two or more independent samples on center, variability, clusters, gaps, outliers, and other features

histograms, side-by-side boxplots

parameter

a numerical summary of a population

normal distribution

A function that represents the distribution of variables as a symmetrical bell-shaped graph.

What are the standard deviations percentages in a normal distribution?

68%, 95%, 99.7%

Define z-score

measures how many standard deviations a data value is from the mean.

z score formula

z=(x-mean)/standard deviation

IQR is ALWAYS a ____ value

single

When the shape of the distribution is approximately normal, describe SOCS

Shape: Approximately/fairly symmetric

Outliers: Q1-1.5(IQR)

Q3+1.5(IQR)

Center: Mean

Spread: Standard Deviation

When the shape of the distribution is approximately skewed left, describe SOCS

Shape: Approximately skewed (strongly) left

Outliers: Q1-1.5(IQR)

Q3+1.5(IQR)

Center: Median

Spread: IQR

When the shape of the distribution is approximately skewed right, describe SOCS

Shape: Approximately skewed (slightly) right

Outliers: Q1-1.5(IQR)

Q3+1.5(IQR)

Center: median

Spread: IQR

Ex. Describe the distribution of # of hours of sleep

3,5,6,6,7,7,7,7,8,8

Shape: The distribution of # of hours of sleep is slightly skewed left

Outliers: (any number below the given answer is an outlier)

Q1-1.5(IQR)

6-1.5(7-6)=4.5

Q3+1.5(IQR)

7+1.5(7-6)=8.5

(4.5 to 8.5 to not be an outlier)

Way to low because 3 is an outlier since 3 is less than 4.5

Center: Median

Median=7

Spread: IQR

7-6=1

association between two variables

correlation; when knowing one affects the other (or helps predict the other)

Mosaic Graphical Effect

the width of each rectangle(bar) is promotional to the # of individuals in the corresponding category

How to find standard deviation on the calculator?

Stats

Calc

1 vars-Stats

Define standard deviation

measures spread by finding he average squared distance of each data value from the mean

Percentiles

p% of the data less than or equal to it

cumulative relative frequency

represents the number or proportion of a data set less than or equal to a given number.

What percentile is Q1?

25th percentile

What percentile is the median?

50th percentile

What percentile is Q3?

75th percentile

When referring to percentiles, we say a value is __ a certain percentile, ___ In a certain percentile

AT, NOT

density curve-area under curve is always =?

1

The Z score is the % to the left or right?

left

Where can you find the z-score?

table A

What is the empirical rule?

68-95-99.7

If a normal probability plot is fairly linear, then the distribution of data is approximately____

normal

A ____tells us what values a variable takes and how often it takes them

distribution

consists of the minimum, Q1, median, Q3 and maximum value of a data set.

5 number summary

If the mean is less than the median in a unimodal distribution, the shape is most likely

skewed right

Two measures of spread are what?

Range, IQR

A relative cumulative frequency plot with areas proportionate to sample size is

mosaic plot

If a data set is approximately Normal,____will be approximately linear.

normal probability

can be used to compare the relative standing of two individuals within their respective distributions.

standardized statistics (z scores)