Introducing Statistics 1, 2, 3: Descriptive Statistics
68 flashcards · Mathematics · by lakesare
[Modelling diagram] Name 4 steps in the modelling process.
Pose a question Collect data Analyse data Interpret results The modelling diagram
[Modelling diagram] Give 1 example of a modelling process. Pose a question Collect data Analyse data Interpret results
Pose - How many large species are there in the sea? Collect - raw data Number of large species discovered by yearAnalyze - the red line A possible model for the discovery curve.This model has been chosen so that the curve flattens out as time goes on, as would be expected with such data. The model goes through the data reasonably well, so it provides an adequate representation of the pattern in the data.Analyse - looking at the model, think of how many large mammals may be there in the sea.
[Modelling diagram] What's the model? The modelling diagramAnalyze the data == create the model
The red line that goes through the data, the formula that underlies the data.
Why is the scatterplot called so?
Because it helps to visualise the pattern (or lack of pattern!) in the scatter of data on the page. A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point.
What is spurious accuracy?
When we have too much unjustified accuracy.
[Stemplot] Why is the stemplot called so?
Because it looks like a tree stem with leaves.
[Stemplot] What does n = 34 mean in a stemplot?
The batch size - number of values in the stemplot.
[Stemplot] What does "26|9 represents 26.9 miles per gallon" mean in a stemplot?
The rule enabling us to combine the level name (26) with the leaf digit (9)
What is this?
A stemplot.
[Stemplot] Where is an outlier? Stemplot of median salaries for highest-paid occupation
11|4 (representing £114,000) is an outlier.
[Stemplot] What do we say about the median and outliers? Stemplot of median salaries for highest-paid occupation11|4 (representing £114000) is an outlier.
Median is resistant to outliers.
[Stemplot] How could we write this stemplot more succinctly?
Make 114 the high outlier. High outlier at £114,000.
[Stemplot] What "LO 21 36" stands for?
Low outlier at £2100, Low outlier at £3600.
[Stemplot] How can we improve this stemplot? Stemplot of mileage of used cars (too many levels).
Reduce the number of levels. Stemplot of mileage of used cars (too few levels). In the stemplots you have drawn so far we have always told you the levels to put on t he stem. Getting the number of levels right is important, since otherwise you may not get a useful impression of the overall shape of the batch.
[Stemplots] What are the modes on this stemplot? Stemplot of moth counts Mount Fuji, Japan
One mode around level 2.
[Stemplots] Visually imagine the symmetric batch.
Stemplot of percentage scores in an English test
[Stemplots] What do you call batch of data which is not symmetric?
A skew.
[Stemplots] Why is this batch of data considered right-skew?
Because its large values are spread out and small values are close together. Right skewness is also often referred to as positive skewness and left skewness as negative skewness. The stemplot turned on its side. The right tail is longer; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed, right-tailed, or skewed to the right, despite the fact that the curve itself appears to be skewed or leaning to the left; right instead refers t…
[Measures of location] What's a location of the batch?
Location of the batch - single representative number for a batch of data.
[Measures of location] What does it denote?
The sum of each x in a batch.
[Measures of location] Name 2 measures of location.
Median Arithmetic mean
What does EL stand for?
Extreme lower.
[Measures of location] How should you picture the median?
[Measures of location] What's the median price of this batch of 10 prices? Prices of 10 digital cameras Prices in order and arranged in a V-shape.
(70 + 74) / 2 = 72.
[Measures of location] What does it denote?
The arithmetic mean.
[Measures of location] What's sensitive VS resistant measure?
sensitive measure - affected by extremes. Mean is a sensitive measure.resistant measure - resistant to extremes. Median is a sensitive measure.
[Measures of spread] What's the range measure of spread? Measures of spread: range, interquartile range, standard deviation.
range = EUPPER - ELOWER
[Measures] What's the measure of location VS measure of spread
measure of location - a single number which represents the overall location of values in a batch. E.g. mean, median.measure of spread - a single number that represents the spread of values in a batch. E.g. range, interquartile range, standard deviation.
[Quantiles] Name 3 common quantiles.
quartile - 4 groups decile - 10 groups percentile - 100 groups Percentile - coined by Francis Galton in 1885, from percent + -ile.Quantile - back-formation from quantity, modeled on percentile.
[Quantiles] Explain the median in percentages.
Median is a 0.5 quantile.
[Quantiles] By definition - what's quantile VS percentile?
quantile - lines that divide the data into some n of equally sized groups. percentile - lines that divide the data into 100 of equally sized groups.
[Quantiles] What are x4 and x12 values called?
x4 - lower quartile x12 - upper quartile The points at the side hinges, in this case x(4) and x(12), are the quartiles. They are denoted Q1 and Q3 respectively.(Sometimes they are referred to as the first quartile and the third quartile.)
[Quantiles] What does Q1 stand for?
Lower quartile.
[Quantiles] What's the value of the lower quartile?
130.
[Quantiles] Why is the upper quartile called Q3?
Because it's 3/4th way to the top.
[Measures of spread] What does IQR stand for?
InterQuartile Range
[Measures of spread] How do we find range VS interquartile range (IQR)? Measures of spread: range, interquartile range, standard deviation.
Range: upper extreme (Eu) – lower extreme (EL). IQR: upper quartile (Q3) – lower quartile (Q1)
[Measures of spread] Why do we prefer interquartile range (IQR) to range? Range: upper extreme (Eu) – lower extreme (EL). IQR: upper quartile (Q3) – lower quartile (Q1) Measures of spread: range, interquartile range, standard deviation.
Because interquartile range is a much more resistant measure of spread.
[Quantiles] By definition - what's quantile VS quartile?
quantile - lines that divide the data into some n of equally sized groups. quartile - lines that divide the data into 4 of equally sized groups.
What's this called?
Five-figure summary Also known as five-number summary.
[Five-figure summary] What does the line represent in the 5-figure summary?
Ordered batch of n values.
[Five-figure summary] What's M in the 5-figure summary?
Median
[Boxplots] Visually imagine how would you draw the boxplot from this 5-figure summary.
[Five-figure summary] What's EL and EU in the 5-figure summary?
EL - Extreme Lower EU - Extreme Upper
[Five-figure summary] What's Q1 and Q3 in the 5-figure summary?
Q1 - Quartile Lower Q3 - Quartile Upper
What's this called?
Boxplot.
[Boxplots] What's the alternative name for the boxplot?
Box-and-whisker plot.
[Boxplots] Visually imagine a boxplot corresponding to this 5-figure summary. 5-figure summary
Boxplot
[Boxplots] What's denoted by the star?
An outlier.
[Boxplots] Name 5 interesting points in the boxplot.
Lower Extreme (EL) Lower Quartile (QL) Median (M) Upper Quartile (QU) Upper Extreme (EU)
[Boxplots] What's the symmetry/skewness of these data?
It's left-skew.
[Earnings of men VS women] What do they mean by the earning ratio at the mean earning ratio at the median?
earning ratio at the mean - mean/mean earning ratio at the median - median/median
[Quantiles] What do we call 284?
"The 10th percentile is 284". The nth percentile is a particular number.
[Quantiles] What exactly is 10th percentile? The nth percentile is a particular number.
10th percentile - such a number, that 10% of the numbers in the batch fall below it.
[Stemplots] Visually imagine the stemplot with the right-skew. Stemplot of percentage scores in an English test
[Boxplots] Visually imagine the boxplot with the right-skew.
[Measure of location] - [Measure of spread] median - _________________________ mean - _________________________
median - interquartile range mean - standard deviation
What is "deviation" short for?
Deviation of the data value from the mean.
What's the formula for deviation?
x_value – batch_mean
Colloquially - deviation VS standard deviation?
deviation - x - xmean per each x. standard deviation - a [measure of spread], a kind of average deviation across the batch.
[Measures of spread: standard deviation] Name 2 reasons why the formula for standard deviation looks like this. Standard deviation is a kind of average deviation across the batch, we could have simply taken the mean of all deviations!
We do √(deviation2 + ...deviation2) so that pos and neg deviations don't cancel out. We do n – 1 because it has better statistical properties than simply n. Sometimes the definition is so that it's just n.
[Measures of spread: standard deviation] What does "s" stand for?
s - standard deviation
[Measures of spread: standard deviation] What does "s2" stand for?
s2 - variance
How can we describe this data more efficiently that listing 50 000 values? For each red blood cell, n of parasites: 1, 4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 (50 000 values). A U.S. government poster from the 1940s aimed at combatting malaria
Use grouped data. Malaria parasites in red blood cells.
[Notation in statistics] How would you expand this Σ notation?
[Measures of spread: standard deviation] How do we denote: standard deviation VS variance?
standard deviation - s, σ variance - s2, σ2 Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter sigma σ, for the population standard deviation, or the Latin letter s, for the sample standard deviation.
[Measures of spread: standard deviation] Visualise high variance VS low variance.
high variance low variance Link to a wonderful simulation: shiny.rit.albany.edu/stat/visualizess.
Visually imagine: boxplot VS stemplot.
boxplot stemplot