Descriptive Statistics

Qualatative Data

data in the form of words, characteristics. etc. (ex> fav color, birthday month)

Quantitative Data

data in the form of numerical values (ex>height, weight)

Discrete Quantitative Data

Limited values that we can count

Continous Quantitative Data

Values over an interval (normal curve)

univariate data

1 variable

bivariate data

studies the relationship between 2 variables

dot plot

quantitative

boxplot

quantitative

histogram

quantitative, bars touch, measures the variable against the frequency

stem and leaf plot

quantitative, needs a key

Cummulative Frequency Plot (ogive)

quantitative, remember when interpretating - it is to the left (say “or less”), 0% = min, 25% = Q1, 50% = med, 75% = Q3, 100% = max, y-axis adds up to 1 (or 100%)

qualitative graphical displays

pie chart, bar chart

distribution definition

a set of data that uses the frequency that each outcome occurs among all possibilities (all of the possible outcomes of your data)

measures of central tendency

where center of distribution of data lies

• mean

• median

• mode (The mode is strictly for qualitative data!! You HAVE to use mean or median for quantitative data !!)

measures of spread

amount of variation in distribution

• range

• IQR

• standard deviation

calculator key

n = sample size

shapes of distribution

• skew right

• skew left

• unimodal

• bimodal

• symmetric 

• uniform

• multi-modal

• skew right

• mean>median>mode

• tail is to the right

• few data points to the right pull the mean up

• unimodal (one peak, one mode)

• skew left

• mean<median<mode

• tail is to the left

• few data points to the left pull the mean down

• unimodal (one peak, one mode)

• symmetric

• bell shape

• unimodal (one peak, one mode)

• mean = median = mode

• uniform

• about same heights

• bimodal

• symmetric vs. nonsymmetric

multi-modal

description: with skewed data use…

• median

  • median doesn’t get affected by outliers/skewedness (unlike the mean)

• IQR

• boxplot

description: with symmetric data use…

• mean

• standard deviation

• histogram

how to make classes on histogram

(not needed)

5 number summary

min, Q1, med, Q3, max

how to find median point

(n+1)/2 

…then count to that point and that is your median (when listed in order)

when making a boxplot…

• create number line to space everything out evenly

• intervals are spaced out in 25%’s (this shows the spread, not the number of points)

• when it is longer, it just means the points are more spread apart from each other (variability)

calculator steps

standard deviation

the average distance each value lies from the mean

• The more points you have in the middle, the smaller the standard deviation. The less points you have in the middle, the larger the standard deviation.

calculating outliers

• outliers fall OUTSIDE of this interval

• can write it as the “usual interval of points”

rules when describing data

1. center

2. spread

3. shape

4. unusual features (gaps, outliers, clusters)

MUST BE IN CONTEXT

symbols

pie chart question

contingency table

2 way table

segmented bar graph

relative frequency vs cumulative relative frequency

• relative frequency: how frequent this number occurs

• cumulative relative frequency: the frequencies but added together as the data moves up

when talking percents

whenever there is “of the __” - that is the denominator

comparitive statements

“greater than, higher, larger, less than, lower, smaller, equal, the same”

Normal Distribution - properties

• symmetric about the mean

• curve approaches the horizontal axis, but never touches or crosses it

• total area under the curve is always equal to ONE

• area under the curve = probability

• The Empirical Rule can be applied for ANY normal distribution

• it is considered UNUSUAL to be more than 2 SD from the mean in either direction

Normal Distribution - graph

• 68% of data lies within 1 SD of the mean

• 95% of data lies within 2 SD of the mean

• 99.7% of data lies within 3 SD of mean

when describing normal distributions, ALWAYS write “approximately” and always state the direction (above/below) you are describing

percentile

• that # and to the left (below)

• The rth percentile is a value such that r% of the observations in the
  data set fall at or below that value

Comparing 2 data sets

• Back to back stem and leaf

• Parallel box plots

• Side by side histograms

• Write comparative statements between distributions

• Include context and suggestions!

z-score

• A z-score tells you exactly how many SD a data value is above or below the mean.

• z-score is positive when data is above the mean

• z-score is negative when data is below the mean

• can only use z-score with normal distribution

calculating probability with z-score

• draw a graph to visually see it

• to the left: refer to formula sheet

• to the right: refer to the formula shete and subtract that from 1

• between: larger value in table - smaller value in table

steps when handling problem w/ z-score

1. write the info (or do a diagram)

2. find z-score (round to 2 decimal places)

3. find probability using table (must have you P statement)

answer in context

quartiles

• Q1 = median of 1st half of data

• Q3 = median of 2nd half of data

How does a shift and multiplier affect the mean (measure of center) or SD (measure of spread)?

• Measures of spread are ONLY affected by multipliers

• Measures of center and individual values are affected by BOTH shifts and multipliers