Statistics Flashcards UNIT 1

the objects described by a set of data

any characteristic of an individual (can take different values for different individuals)

places an individual into one of several groups or categories (example: male vs. female). This data is COUNTABLE

takes numerical values for which arithmetic operations make sense (measurable)

tells us what values the variable takes and how often it takes these values - pattern of variation (table, bar, graph, pie chart, etc.)

an extreme value that differs greatly from other values in a set of values

a graph of qualitative data; a quick way to visualize a set of data

the digit(s) in the greatest place value(s) of the data values are the stems. the digits in the next greatest are the leaves.

use key

4|2 = 42

eac stem is listed more than once

• first stem number: 0-4’s

• second stem number: 5-9’s

describing or interpreting quantative data distributions.

*All of these with context —use question to answer the question! (WRITE THEM ALL OUT)

• example

  • S - skewed to the left; unimodal

  • O - maybe at 40

  • C - median 85

  • range 60

  • The distribution of quiz scores is unimodal and skewed to the left. There is a possible outlier of 40. The center of the distribution is the median at 85 and the range of the quiz scores is 60.

a visual description of what the distribution looks like

• a distribution is symmetric if the right and left sides of the histogram are approximately mirror images

• is it skewed?

• clusters? (unimodal, bimodal, trimodal?)

if a distribution extends much further from the right side than the left

***The tail is to the right

if a distribution extends much further from the left side than the right

***The tail is to the left

one cluster

two clusters

more than two clusters

If looking at a histogram with no data, use words like

IQR = Q3-Q1

• used to determine if an outlier exists

if you have a histogram with data

a value that divides the observations so that about half takes longer larger value and about half take smaller values

USE MEDIAN

the arithmetic average of a data set

• the sum of all the values divided by the number of values

***USE THIS FOR CENTER

the middle value of a data set; the equal areas part, where 50% of the data are at or below this value and 50% of the data are at or above this value

describes the variability of the data

• range (histogram with no data)

histogram with data

• variance

• standard deviation

• IQR

(max-min)

***ONLY USED THIS FOR HISTOGRAM WITH NO DATA

the count of how often something occurs

percentage or proportion of the whole number of data

• frequency/total number

breaks the range of values of a variable into intervals and displays only the count or percent of the observations that fall into each interval

1. divide the data into classes (intervals) of equal width

   1. need to specify classes so that each individual falls into one class

   2. usually will need between 5 and 7 intervals

2. each bar of the histogram can include only one of its endpoinrs

3. intervals should NEVER overlap

4. LABEL AND SCALE YOUR AXIS

5. !!!!!!!title your graph!!!!!

class width = (max-min)/number of groups

1. enter the data into L1

2. 2ND stat plot (above y=) → plot1 → ENTER

3. Turn on → choose symmetric histogram picture → graph → zoom9

4. window → fix xscale=_____

5. Hit TRACE for interval

if not starting at zero when its on a graph

round to

plot each observation against the time at which it was measured - time is always on the z-axis

STAT → CALC → 1 Var Stats

Min

Q1

Med

Q3

Max

Inner Quartile Range

Q3-Q1

1. find IQR (Q3-Q1)

2. Q1-1.5(1=IQR); Q3+1.5(IQR) → [ __ , __ ]

3. Any number outside this interval is an outlier

a statistic is resistant if adding an extreme value does NOT change the value of the statistic much

• A mean is NOT resistant, a MEDIAN is

DO NOT USE BOXPLOTS FOR A SHAPE, alway use histograms

• Boxplots are good fo five number summary

DO NOT USE BOXPLOTS FOR A SHAPE, alway use histograms

• Boxplots are good fo five number summary

DO NOT USE BOXPLOTS FOR A SHAPE, alway use histograms

• Boxplots are good fo five number summary

close together

“typical” value, which we migh describe by the median

the mean and median are exactly the same

usually further out in the long tail than the median is

• The mean is pulled toward the skew and outliers

The whiskers only extend to adjacent values, not outliers

• Hitting TRACE will show all points

One of the most common measures of spread. It looks as how far each deviation is from the mean.

• Measuring spread: STANDARD DEVIATION

=observation-mean

add all the numbers and divide by the sum

1. Calculate the mean

   1. add all the numbers and divide by the sum

2. Calculate each deviation

   1. deviation=observation-mean

3. Square each deviation

4. Find the “average” squared deviation

   1. Calculate the sum of the squared deviations divided by the degrees of freedom (n-1) - This is called the VARIANCE

5. Calculate the square root of the variance, this is the STANDARD DEVIATION

The average square distance

• (sum of square deviations)/(n-1)

measures the spread about the mean

is the is sample standard deviation

NOT RESISTANT

• ALWAYS greater than or equal to 0

• Sx=0 ONLY when there is no variability

0

there is no variability

has a symmetric shape

No, Sx is not resistant. It is even less resistant than mean to extreme outliers.

parameter (population SD)

if you are looking for a statistic (sample SD)

• mean and standard deviation

or

• median and IQR

are usually better than the mean and standard deviation for describing a SKEWED DISTRIBUTION or a distribution with outliers

symmetric distibutions that don’t have outliers

• Note: numerical

the distribution is skewed to the right

knowing the mean or median is helpful, but sometimes you want to know where something falls with respect to everything else…

• The pth pecentile of a distribution is the value with p percent of observations at or below it

• [(number of values below x)/(number of total values)] x 100

• If it says “justify your answer”, use 1.5IQR method

[(number of values below x)/(number of total values)] x 100

A graph that displays the cumulative relative frequency of each class of a frequency distribution

• (cumulative frequency)/sample size

Tells use how many standard deviations from the mean an observation falls and in what direction

• If x is an observation from a distribution that has a known mean and standard deviation, the standardized value of x is:

  • z=(x-mean)/SD

individuals in different distributions

• not measured in the same units as the original data

• it is the number of standard deviations away from the mean

• positive z-scores are above the mean

• negative z-scores are below the mean