AP STATS U1

Quantitative Variable

A variable that takes numerical values for a measured quantity

Discrete Variable

Takes on a countable number of values with gaps (shoe size)

Infinite Variable

Can take on infinitely many values with no gaps and cannot be counted. (Height)

Dot Plot

Shows every value in the data set as a dot

• ADV= Easy to see the shape of the distribution

• CONS= Hard to make for large data sets

Stem and Leaf Plot

Shows every data value with a stem (beginning number) and a leaf( tens digit). Can also be made back to back with 2 data sets to easily compare them.

• ADV= Easy to see shape of data set

• CON= Hard to make for large data sets

Histogram

A histogram is a graphical representation of the distribution of numerical data, where the data is grouped into bins or intervals. The height of each bar indicates the frequency of data points within each bin.

• ADV= Provides a simple way to visualize data distribution

• CON= Doesnt show each value in the data set due to grouping

DIFFERENT THAN A BAR CHART BECAUSE THE BARS ARE TOUCHING AND ARE CONTINUOUS. BAR CHARTS ARE USED TO MEASURE CATEGORICAL DATA AND HISTOGRAMS ARE USED FOR QUANTITATIVE DATA.

Shape

Describes the overall shape of the data set, could be skewed, uniform, bimodal, unimodal.

Outliers

A feature that is clearly different than the rest of the data set.

IF THERE IS NO INDIVIDUAL DATA YOU GUESS AND SAY IT IS A POTENTIAL OUTLIER.

Center

A value that divides the data so that half of the data is the upper values and the other half is the lower values.

• Skewed left= mean<median

• Skewed right= mean>median

Spread

Measures how far apart the values in the data set are.

• Can use IQR or Range to measure

Mean

The sum of all the data values divided by the number of values.

MEAN IS NON RESISTANT, MEANING IT GETS AFFECTED BY OUTLIERS

Median

The middle value of a data set

NON RESISTANT MEANING IT DOESNT GET AFFECTED BY OUTLIERS.

MEDIAN IS MORE RELIABLE THAN MEAN

Q1

The first quartile, where 25% of the data is at or below it

DO NOT INCLUDE THE MEDIAN

Q3

The third quartile, the value where 75% of the data is at or below it.

DO NOT INCLUDE THE MEDIAN

Range

Difference between the max value and the min value

IQR

Difference between the Q3 and Q1.

USE THIS IF YOU HAVE DATA

Standard Deviation

Typical distance that each value is from the mean

USE IF YOU HAVE DATA

Variance

The square of the standard deviation

Determining outliers

IQR Method= Q1- 1.5(IQR) or Q3+ 1.5(IQR)

Also 2 stdev’s above or below the mean.

How do outliers affect summary stats?

It pulls the mean, stdev, and range lower.

DOESNT GREATLY AFFECT MEDIAN AND IQR

5 number summary

Min, Q1, Med, Q3, Max

Box plot

A box plot is a graph that displays the distribution of a data set using the five-number summary: minimum, Q1, median, Q3, and maximum.

50% of the data lies within the box, 25% to the left, 25% to the right

Frequency

The count of how often something occurs

Relative frequency

Proportion of the whole number of data.

freq/total number of data points

How to make a histogram on a calculator

Stat- edit- L1

2nd- y(stat plot)- turn on histogram- zoom- zoom stat (9)

To adjust width go to window and change x scale

trace gives you interval min and maxes

Choosing measures of spread

• Median and IQ= Good for skewed data or data w/ outliers bc they are resistant

• Mean and SD= Good for symmetric data bc it is non resistant

Linear Transformations

Multiplying a value to data changes every summary stat

Adding or subtracting data affects everything but IQR and SD

MULTIPLYING CHANGES SHAPE OF DATA

Percentiles

The percent of observations at or below an observation

count how many observations are at the value or below and divide it by the number of observations

Z score

How many standard deviations something falls from the mean and in what direction.

X- mean/SD

Rescales original distribution so that the mean is 0 and SD is 1

Density Curves

Smoothes out irregularities of histograms (curve of best fit)

Always on/above x axis

Has an area of 1 under it

Median= equal areas point

Mean= Balance point

Normal Curve

A DC that is symmetrical, Unimodal, and bell shaped.

USE MEAN AND SD TO DESCRIBE