UNIT 1 MIXED Flashcards
How do you find the median from
an 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 is the couse “Statistics” about?
The study of variability. Not just how individual subjects vary, but later on how two different samples from the same population can get different summaries. We later look at how statistics vary from sample to sample.
Think of the minimum value, the median and the IQR, which is impacted by shifting (adding a constant?)
adding a value shifts the entire histogram to the right, so the min and the median will increase by that amount, BUT THE IQR WILL NOT CHANGE.
When drawing a graph or chart, what do you have to remember to do?
LABEL AXES, make a KEY(if needed ) AND GIVE IT A NAME!!! “Figure 1: Age and Food Preference”
What symbols do we use for population mean and sample mean?
Mu for population mean, xbar for sample mean.
conditional distribution?
A distribution 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.
If I take a random sample 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them… and the average number of pickles was 9.5, then 9.5 is considered a _______?
statistic. It is a summary of a sample.
How can you describe the center of a distribution?
OPTIONS: give the mean (balance), median (splits area in half), mode (peaks, if bimodal talk about both modes) or say “centered around ____”
If you want to calculate % above a value, what do you put into normcdf(? ?)
find z score for value, and then normcdf (Z left, 999)
What is variability?
Differences, how things differ. There is variability everywhere. We all look different, act different, have different preference. Statisticians look at these differences. SAMPLE STATISTICS ALSO VARY FROM SAMPLE TO SAMPLE.
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.
What percent of the data is below the median?
50%
If the distribution is skewed (or outliers/not symmetric) what would you use for center and spread statistics?
Median (center) and IQR (spread)
What do you call things that are not independent?
associated. Or not independent. We generally don’t say DEPENDENT (unless talking about y variable on a scatterplot).
Think of the minimum value, the mean and the standard deviation, what is impacted by shifting (adding a constant)
adding a value shifts the entire histogram to the right, so the min and the mean will increase by that amount, BUT THE SD WILL NOT CHANGE.
If you want to find % below a value, what do put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright)
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 do you find summary statistics (mean, st. dev, median, 5 number summ)
stat>calc> 1-VarStats (if frequency table, be sure to do 1-var stats L1, L2)
If a distribution is skewed right, what will be greater, the mean or median? WHY?
Mean. The mean moves further to the right 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
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”
For information purposes, which gives most… stem-leaf, histogram or box-whisker?
Stem leaf gives the actual values and the shape… histogram just the shape… and box-whisker the least amt, but are great for comparing multiple distributions.
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.
How can you turn OGIVES into histograms?
RECTANGLE DROP! (bin drop)
For information purposes, which gives LEAST… stem-leaf, histogram or box-whisker?
Box/Whisker, BE CAREFUL. you really don’t know how things are distributed. The box and whisker and fish tank give a very GENERAL look.
Does a census make sense?
A census is ok for small populations (like Mr. Nystrom’s students) but impossible if you want to survey “AVERAGE TREE HEIGHT IN THE US”
When there is a relationship between two variables, we say that they are
associated (or not independent)
What does SHIFT and SCALE mean?
Shift is when you add or subtract, scale is when you multiply
What is a contingency table?
shows distributions across 2 variables like gender and music pref. AKA 2-way table
How do you match OGIVES to histograms?
RECTANGLE DROP!!
What is a frequency distribution?
A table, or a chart, that shows how often certain values or categories occur in a data set.
What is the total area under the normal curve?
1 or 1.000 (or 100%)
If the distribution is unimodal and symmetric, what would you use for center and spread statistics?
Mean (center) and Standard Deviation (spread)
When can you round?
AT THE VERY END!!! (keep 3 digits until end!)
How are mean, median and mode positioned in a skewed right histogram?
mode- median- mean (mean chases the tail)
Think of the minimum value, the mean and the standard deviation, what is impacted by shifting (adding a constant)
If you multiply a data set by a number, then the min, mean and the SD will multiply by that number.
What do we sometimes call a categorical variable?
qualitative
the output for normcdf(Zleft, Zright) is_______
the area under the normal curve between the given z scores
What symbols do we use for population standard deviation and sample standard deviation?
Sigma for population and s for sample.
what is a clear example of the median’s resiliance and when you would use the median instead of the mean?
Imagine the amount of money in peoples pockets: {1, 2, 2, 5, 5, 8, 8, 9}. The mean and median are both 5. You might say “the average person in this group had 5 bucks.” But imagine if the 9 was actually 9000 (1, 2, 2, 5, 5, 8, 8, 9000}, in this case, the median would still be 5, but the mean goes up to over 1000. If asked about the average person, would you say 5 bucks or 1000 bucks? I think 5 is a better description of the average person in this group and the 9000 is simply an outlier. When there are outliers or skewed data, use the median.
Can numbers be CATEGORICAL?
sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes… these are categorical.
If the mean is above the median, the distribution may be
skewed right or positively skewed, the mean follows the tail
How do you find relative frequency?
PERCENTS- just divide frequency by TOTAL. a percent is relative to the whole.
What are the displays you can use for CATEGORICAL DATA?
bar chart, pie chart, segmented bar chart,
What is the median?
(a point estimate) the middlest number, it splits area in half . Always in the POSITION (n+1)/2
How can you describe shape?
TWO THINGS: modes and symmetry.
unimodal, bimodal, multimodal AND uniform, symmetric, skewed
what is the shortcut invnorm?
gives data value from percentile, skips Z score. Invnorm (percentile, mean, sd)
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 parameters do you usually calculate for categorical data?
mean (and sd)
How do you describe CENTER for bimodal or multimodal?
talk about the modes (the lumps, the clusters)
what happens if you multiply all of a data set by a constant? Think of an example
it is scaled Both center and spread are impacted. Mean/ median/ stand dev/ iqr/ quartiles all multiplied by that constant. Center, spread and all individual values are changed. Consider 1,2,3,4,5 mean of 3 and range of 4. Now multiply by 3: 3,6,9,12,15 and you get a mean of 9 and a range of 12… both multiplied by three.
What percent of the data is above Q3?
25%
what is the shortcut normcdf?
gives % from raw data, skips Z score. normcdf (low VALUE, high VALUE, mean, sd)
When there is no relationship between two variables, we say they are
independent (or not associated)
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.
How do you find percentiles and make a boxplot from OGIVE?
Go across till you hit the curve and then STRAIGHT DOWN!
What percentile is Q1?
25th
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)
If you want to find percentile for a value, what do you put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright) like going from negative infinity up to the z score
not associated is the same as being ____________
independent
Which calculator function gives you a z score?
invnorm(%ile)
What symbols do we use for population proportion (%) and sample proportion (%)?
p for population and p-hat for sample
Give an example of independent variables
If 80% prefer cheese and only 20% prefer pepperoni IN EACH GRADE AT BHS…then they all have the same preference, so grade doesn’t matter. We say “school year and pizza choice are independent”
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).
What percentile is the median (aka Q2)?
50th
what display could you use to compare two quantitavive data sets?
side by side stem/leaf, histograms or box whiskers, or back to back stem/leaf or histogram, two ogives on same graph,
What is quantitative data?
The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.
How can you describe shape?
unimodal, bimodal, multimodal, uniform, symmetric, skewed
What is a Z score?
The number of standard deviaiton away from the mean
Gender and Video Game playing are___________ because_______
associated (or not independent) because a higher percentage of males play video games. (think.. It depends on gender)
if you are calculating a percent, then you must have _____ data
categorical
not independent is the same as being ____________
associated
