ap stats 1.1-1.4

skewed to the right means…

right tailed, peak to the left (mean gets affected by the pos outliers, but the median doesn’t so, mode < median < mean)

skewed to the left means…

left tailed, peak to the right (the mean gets affected by the neg outliers, but the median doesn’t so, mean < median < mode)

negative outliers

neg outlier < Q1 - 1.5(Q3 - Q1)

positive outliers

pos outlier > Q3 + 1.5(Q3 - Q1)

measures of center

mean, median, mode

measures of spread

stdev (summation/n-1), range, IQR (Q3 - Q1)

Q1 (the lower quartile)

the value below which 25% of the data falls. it separates the lowest 25% of the data.

inter quartile range (IQR)

(Q3 - Q1): it represents the spread of the middle 50% of the data

5 number summary

min, q1, med, q3, max

when are boxplots appropriate?

when we want to capture the spread of the data (also when we’re interested in the median)

what are boxplots used for?

comparing sets of data (also, always include description of the center and spread. and non modified boxplots don’t usually indicate outliers)

modified boxplots/ box and whisker plot

they indicate outliers

what’s a statistic association?

when the value of one variable impacts the other

the explanatory variable is like the…

independent variable, which is the variable that is manipulated

the response variable is like the…

dependent variable, which is the outcome

3 key components when describing an association

1) state if there’s an association between the explanatory and response variable

2) back up your answer with numbers

3) bring back the context (mention and describe the 2 og variables)

what u must do when making a graph

have a title, scale and label on both axises, and label the 2 variables?

standard deviation sample\sqrt{\frac{\Sigma\left(x\imaginaryI-\operatorname{mean}\right)^2}{n-1}}

population denominator is just n (the number of data points)

why do u have to change the denominator when finding the standard deviation of a sample?

because the sample can sometimes not be representative of the population

population mean

μ

stdevp

σ (or on calc: σx)

pop variance

\sigma^2

an observation/data point

Xᵢ

sample mean

x̄

stdev (sample)

S (or on calc: Sx)

sample variance (x/b-1)

S^2

symmetric graphs

the mean, median, and mode are all equal or close to equal

gaps in the distribution are

breaks between data points

When u see an outlier, u should always…

comment on them (however, most of the time they’re removed)

bimodal

when a graph has two modes or 2 distinct peaks

clusters

noticeable clumps or groupings of data

what words can u use to describe the shape of a graph?

skewed, symmetrical (mean=mode=median), unimodal (1 peak/mode), uniform (rectangular shaped), bimodal (2 high peaks/ modes)

resistant/robust stats

those that are not heavily influenced by outliers

the measures of central tendency that are resistant/robust are…

median, mode, IQR

the measures of center (tendency?) and spread that are non resistant (meaning they’re susceptible to changing if there are outliers)

mean, stdev (pop and sample), variance, range

measures of dispersion

variance , stdev (p and s), and more?

how to describe a distribution of data

SOCS:

• shape (skewed, symmetric, unimodal, bimodal, or uniform)

• outliers (neg <Q1 - 1.5IQR or pos >Q3 + 1.5IQR)

• center (mean, median, mode)

• spread (range, IQR (q3 - q1), stdev (p and s), and both variances)

categorical data

qualitative data that doesn’t represent a numerical value

numerical data

data that represent numerical values

the explanatory variable…

influences changes in the response variable

1 variable graphs

dotplots, charts (like bar or pie), and more!

2 variable graphs

side by side + segmented bar graphs

graphs for quantitative data

histograms, stem and leaf plots, and more

graphs for qualitative data

bar graphs

possibility (can it happen at all?)

• if the outcome has a probability greater than 0

plausibility (is this outcome reasonable to believe, given the evidence?)

• stronger than possiblilty

• based on p value (if the p value is less than 0.05 than we can reject the null hypothesis)

likelihood

below 40% isn’t that likely

uniform graphs

no peaks or mode really

a normal distribution

bell shaped, symmetric, unimodal, mean = mode = median