# UNIT 1 FIXED - MIXED Flashcards

What is the difference between popluation of interest, variable of interest and parameter of interest?

If we want the average weight of cape cod dogs, population is cape cod dogs, the variable is the weight, the parameter is the mean weight. If we wanted the percent that are brown, the population would still be cape cod dogs, the variable would be dog color and the parameter would be % brown.

What symbols do we use for population proportion (%) and sample proportion (%)?

p for population and p-hat for sample

What is meant by relative frequency?

The PERCENT of time something comes up (frequency/total)

How can you turn OGIVES into histograms?

RECTANGLE DROP! (bin drop)

If you want to find the value that is in the top 7 percent, what do you do?

use INVNORM(.93)

What is the difference between discrete and continuous variables?

Discrete can be counted, like “number of cars sold” they are generally integers (you wouldn’t sell 9.3 cars), while continuous would be something like weight of a mouse. 4.344 oz. Summaries of discreet variables will often be decimals.

Does the IQR capture 68% of the data?

NO. it catches the middle 50%.

What percentile is the median (aka Q2)?

50th

Make a guess as to what relative cumulative frequency is…

It is the ADDED up PERCENTAGES.. An example is selling candy, 25 pieces sold overall, with 10 the first hour, 5 the second, 3 the third, and 7 the fourth hour, we’d take the cumulative frequencies, 10, 15, 18 and 25 and divide by the total giving cumulative percentages, .40, .60, .64, and 1.00. Relative cumulative frequencies always end at 100 percent.

what is a conditional distribution?

A distribution with a condition (within the table), along only one row or one column… NOT IN THE MARGINS. You are given a condition.. Then read along that row or column.

How can you think about the mean, median and mode remember the difference when looking at a histogram?

mean is balancing point of histogram, median splits the area of the histogram in half, mode is the highest point or points

Association and Independence. How are they related?

Variables are either independent or associated. Meaning: if one impacts the other then we say there is an association. If not, Then they are independent.

what is the shortcut normcdf?

gives % from raw data, skips Z score. normcdf (low VALUE, high VALUE, mean, sd)

Can numbers be CATEGORICAL?

sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes… these are categorical.

How do you find Q1 and Q3?

Q1 is the median of the bottom half and Q3 is the median of the upper half (they are the 25th and 75th percentiles)

What are the percentiles for Q1, med, and Q3?

25, 50 and 75

not associated is the same as being ____________

independent

What is the mean?

(a point estimate) the old average we used to calculate. It is the balancing point of the histogram

What does SHIFT and SCALE mean?

Shift is when you add or subtract (it slides the histogram left and right), scale is when you multiply

When can you round?

AT THE VERY END!!! (keep 3 digits until end!)

Which calculator function gives you a z score?

invnorm(%ile)

where are the “outlier fences?”

1.5 IQR above Q3 and 1.5 IQR below Q1. Just a rule of thumb.

Another name for “skewed right” is

positively skewed

What is frequency?

How often something comes up

What is categorical data?

The actual individual category from a subject, like “sedan” or “blue” or “female” or “sophomore”

How are mean, median and mode positioned in a skewed right histogram?

mode- median- mean (mean chases the tail)

which calculator function gives you a percent?

normcdf(Z left, Z right)

What is the total area under the normal curve?

1 or 1.000 (or 100%)

What is the IQR?

Interquartile range… a measure of spread. Q3-Q1. The distance from Q1 to Q3. The regular range is Hi-Lo, this is the inner range, the interquartile range.

What percent of the data is between Q1 and Q3?

50%

Use the following words in one sentence: population, parameter, census, sample, data, statistics, inference, population of interest.

I was curious about a population parameter, but a census was too costly so I decided to choose a sample, collect some data, calculate a statistic and use that statistic to make an inference about the population parameter (aka the parameter of interest).

What symbols do we use for population standard deviation and sample standard deviation?

Sigma for population and s for sample.

associated is the same as __________

not independent

Think of the minimum value, the mean and the standard deviation, what is impacted by multiplying all data in the set by a constant (scaling)?

If you multiply a data set by a number, then the min, mean and the SD will multiply by that number.

independent is the same as __________

not associated

Compare data to parameters

Data is each little bit of information collected from the subjects. They are the INDIVIDUAL little things we collect, like “5, 7, 9” . if we have all of the data from the population, then we can summarize it by finding the average and that would be called a parameter. (if we only had a sample then the summary is called a statistic)

How does multiplying by a constant impact the summary statistics of a data set? (or random variable)

It is SCALED. Both center and spread are effected. They all (mean, median, IQR, SD, range) get multiplied by three. (BE CAREFUL, remember the variance is the SD squared, so the variance gets multiplied by 9).

If the distribution is bimodal or multimodal, what would you use for center and spread statistics?

Talk about each mode (center) and maybe use the range or IQR. You could also say “one group seems to go from __ to __ and the other from about __ to __”

Why don’t we just use the average (mean) all the time? (instead of mode and median)

The word average is a general term that can be actually talking about the mean, median or mode. We don’t always use the mean because it is not RESILIENT, it is impacted by skewness and outliers

What are 2 major branches of AP STATS?

Inferential and Descriptive

What does GSOCS stand for?

Gaps Shape Outliers Center Spread. I usually say “shape, center, spread, strange” SCSS

What is the difference between categorical VARIABLES and categorical DATA?

The Variable is the overall category. Like “EYE COLOR”. The data is the actual measurement from the subjects. Like “blue, brown, blue”

How do you find the median fro man OGIVE?

go halfway up the y axis, then shoot across to the curve, then straight down. It’s at the 50th percentile (halfway up)

What parameter do you usually calculate for categorical data?

%, percent, or proportion

What is the mode?

(a point estimate) the peaks of a histogram (the humps). or with categorical data, the most popular category

How do you match OGIVES to histograms?

RECTANGLE DROP!!

marginal distribution

distribution in the margins (outside of the table). The overall distributions of a single variable in contingency table.

How do you describe SPREAD for bimodal or multimodal?

talk about the outer edges of the clusters “from here to here” or use the IQR.

Compare Descriptive and Inferential STATS

Descriptive explains you about the data that you have, inference uses that data you have to try to say something about an entire population….

When drawing a normal model, what are the PERCENTILES from left to right?

2.5, 16, 50, 84, 97.5

are any populations actually normal?

no, nothing is normal, just normalish. The only normal thing is the model we use.

If the distribution is unimodal and symmetric, what would you use for center and spread statistics?

Mean (center) and Standard Deviation (spread)

Compare population to sample

populations are generally large, and samples are small subsets of these population. We take samples to make inferences about populations. We use statistics to estimate parameters.

When we say “the average teenager” are we talking about mean, median or mode?

It depends, if we are talking height, it might be the mean, if we are talking about parental income, we’d probably use the median, if we were talking about music preference, we’d probably use the mode to talk about the average teenager.

the output for normcdf(Zleft, Zright) is_______

the area under the normal curve between the given z scores

what happens if you ADD a constant to each value in a data set?

it is SHIFTED only. Does not impact spread. This effects all of the data values and measures of center (mean, med) and quartiles, deciles, etc, IT DOES NOT CHANGE THE SPREAD! (IQR, St Dev, Range all stay the SAME).

What is a categorical variable? Compare to categorical data.

Categorical (or qualitative) variables are the categories you are interested in like “hair color” and “music preference”. The data are the measureds from individuals like: SUV, sedan, Listens to Hip Hop, Female, yes, no, etc.

What parameters do you usually calculate for quantitative data?

mean (and sd) or median (and IQR)

How could you use mode with categorical variables?

With categorical variables. For instance, to describe the average teenagers preference, we often speak of what “most” students chose, which is the mode. “the average teenager likes mexican food.” It is also tells the number of bumps in a histogram for quantitative data (unimodal, bimodal, etc…).

How do you find 5 number summary from OGIVE?

Split the y axis into quarters. Shoot out to the right from 0, .25, .50, .75 and 1.00 till you hit the line in the ogive, then go straignt down. Those numbers on the x axis below correspond to the 5 numbers.

What is the difference between a parameter and a statistic?

BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS. But pppp parameters come from pppp populations, sss statistics come from ssss samples

What is a population?

(not necessarily people). the group of stuff you’re interested in. It could be “bags of potato chips..” Sometimes it’s big, like “all teenagers in the US” other times it is small, like “all AP Stats students in my school”

what is the emperical rule?

mean 68-95-99.7 yeah!

If a distribution is skewed left, what will be greater, the mean or median? WHY?

Median. The mean moves left to keep balance.

mean/SD/median/IQR. How do I know which ones to use?

when unimodal and symmetric, mean and sd. If skewed or outliers? Median and IQR. If bimodal? Talk about the MODES

Compare DATA-STATISTIC-PARAMETER using CATEGORICAL example

Data are individual measures… like meal preference: “taco, taco, pasta, taco, burger, burger, taco” Statistics and Parameters are summaries. A statistic would be “42% of sample preferred tacos” and a parameter would be “42% of population preferred tacos.” Notice that for categorical variables, the categories are words and the statistics and parameters are percents.

What is the difference betwen a categorical variable and categorical data?

If you wanted the percent of cape cod dogs that are brown, the variable would be “dog color” and the data would be: brown, black, white, mixed, brown

what is a nice mean/median/mode helper diagram?

Sketch a skewed left distribution, then mean/median/mode will be labeled in order from L to R

How do you describe SPREAD for skewed distributions (or distributions with outliers?)

Use the IQR

are there any normal samples?

no, nothing is normal, just normalish. The only normal thing is the model we use.