Data Distributions and Statistical Measures flashcards

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Frequency-weighted totalsFrequency Tables, Dot Plots, and Histograms: Repeat each value as often as its frequency says.
When should I use frequency totals?Frequency Tables, Dot Plots, and Histograms: Add frequencies to find a sample size.
What method supports frequency-weighted totals?Frequency Tables, Dot Plots, and Histograms: data sum=Σ(value×frequency)
Read a cumulative countFrequency Tables, Dot Plots, and Histograms: Identify the requested bins before summing.
Frequency totalsFrequency Tables, Dot Plots, and Histograms: Count observations, not labels.
What must I check in frequency tables, dot plots, and histograms?Frequency Tables, Dot Plots, and Histograms: Frequency counts are not data values; histogram interval endpoints must be interpreted consistently
What method supports read a cumulative count?Frequency Tables, Dot Plots, and Histograms: selected count=sum of relevant frequencies
What method supports frequency totals?Frequency Tables, Dot Plots, and Histograms: sample size=Σfrequencies
When should I use frequency-weighted totals?Frequency Tables, Dot Plots, and Histograms: Compute a data sum from value-frequency pairs.
When should I use read a cumulative count?Frequency Tables, Dot Plots, and Histograms: Combine selected bins from a distribution.
Recover a missing observationMean, Median, Mode, and Range: Use totals for a mean and endpoints for a range.
When should I use mean and total?Mean, Median, Mode, and Range: Relate the arithmetic mean to the sum and count.
What method supports recover a missing observation?Mean, Median, Mode, and Range: missing value=n·mean−known sum; range=max−min
Median and modeMean, Median, Mode, and Range: Median is in the middle; mode repeats most.
Mean and totalMean, Median, Mode, and Range: Mean is total divided by how many.
What must I check in mean, median, mode, and range?Mean, Median, Mode, and Range: Sort before finding a median; for even counts average the two middle values; a data set may have no unique mode
What method supports median and mode?Mean, Median, Mode, and Range: even-count median=(two middle values)/2; mode=most frequent value
What method supports mean and total?Mean, Median, Mode, and Range: mean=Σx/n, n>0
When should I use recover a missing observation?Mean, Median, Mode, and Range: Use a mean or range condition to recover an unknown value.
When should I use median and mode?Mean, Median, Mode, and Range: Find the middle or most frequent value using the appropriate definition.
Weighted frequenciesWeighted Means and Combined Groups: Frequency is how many times to include each value.
When should I use weighted mean?Weighted Means and Combined Groups: Combine two groups by their sizes.
What method supports weighted frequencies?Weighted Means and Combined Groups: weighted mean=Σwᵢxᵢ/Σwᵢ
Unknown subgroup meanWeighted Means and Combined Groups: Remove the known group total before averaging what remains.
Weighted meanWeighted Means and Combined Groups: Multiply each mean by how many it represents.
What must I check in weighted means and combined groups?Weighted Means and Combined Groups: Weights represent counts or proportional importance; do not average subgroup means unless their sizes are equal
What method supports unknown subgroup mean?Weighted Means and Combined Groups: m₂=[(n₁+n₂)M−n₁m₁]/n₂
What method supports weighted mean?Weighted Means and Combined Groups: combined mean=(n₁m₁+n₂m₂)/(n₁+n₂)
When should I use weighted frequencies?Weighted Means and Combined Groups: Interpret unequal repetition as weights.
When should I use unknown subgroup mean?Weighted Means and Combined Groups: Use the combined total to recover a subgroup total.
Outlier fencesQuartiles, Interquartile Range, and Box Plots: Find the fence before deciding whether a value is unusually far away.
When should I use quartile interpretation?Quartiles, Interquartile Range, and Box Plots: Read the interquartile range from stated quartiles.
What method supports outlier fences?Quartiles, Interquartile Range, and Box Plots: upper fence=Q₃+1.5(Q₃−Q₁)
Quartiles from a short listQuartiles, Interquartile Range, and Box Plots: Find the middle of each half after sorting.
Quartile interpretationQuartiles, Interquartile Range, and Box Plots: Subtract the lower quartile from the upper quartile.
What must I check in quartiles, interquartile range, and box plots?Quartiles, Interquartile Range, and Box Plots: This course uses medians of the lower and upper halves excluding the overall median for odd counts; supplied box-plot quartiles take precedence
What method supports quartiles from a short list?Quartiles, Interquartile Range, and Box Plots: Q₁=median(lower half); Q₃=median(upper half)
What method supports quartile interpretation?Quartiles, Interquartile Range, and Box Plots: IQR=Q₃−Q₁
When should I use outlier fences?Quartiles, Interquartile Range, and Box Plots: Apply a stated IQR-based outlier rule.
When should I use quartiles from a short list?Quartiles, Interquartile Range, and Box Plots: Use the specified median-of-halves convention.
Compare equal-center distributionsComparing Spread and Standard Deviation: Look at how far the values sit from their common center.
When should I use translation and spread?Comparing Spread and Standard Deviation: Determine the effect of adding the same constant to all observations.
What method supports compare equal-center distributions?Comparing Spread and Standard Deviation: larger squared deviations imply larger standard deviation at fixed n
Scaling and spreadComparing Spread and Standard Deviation: Stretching the data stretches its spread by the same magnitude.
Translation and spreadComparing Spread and Standard Deviation: Moving the whole data set does not stretch it.
What must I check in comparing spread and standard deviation?Comparing Spread and Standard Deviation: Standard deviation is nonnegative and measures spread around the mean; compare or transform it without requiring long manual computations
What method supports scaling and spread?Comparing Spread and Standard Deviation: SD(kX)=|k|SD(X)
What method supports translation and spread?Comparing Spread and Standard Deviation: SD(X+c)=SD(X)
When should I use compare equal-center distributions?Comparing Spread and Standard Deviation: Identify greater dispersion without computing each variance.
When should I use scaling and spread?Comparing Spread and Standard Deviation: Scale standard deviation by the absolute value of a multiplier.
Outliers and resistanceOutliers and Changes to Data Sets: A faraway extreme pulls the mean but may leave the middle position alone.
When should I use replace one value?Outliers and Changes to Data Sets: Update a mean after a single observation changes.
What method supports outliers and resistance?Outliers and Changes to Data Sets: median depends on order; mean depends on total
Append an observationOutliers and Changes to Data Sets: A new entry changes how many values share the total.
Replace one valueOutliers and Changes to Data Sets: Share the one-value change across the same number of observations.
What must I check in outliers and changes to data sets?Outliers and Changes to Data Sets: A change to one observation can affect the mean even when the median stays fixed; distinguish replacing from adding an observation
What method supports append an observation?Outliers and Changes to Data Sets: new mean=(nM+x)/(n+1)
What method supports replace one value?Outliers and Changes to Data Sets: new mean=old mean+(new−old)/n
When should I use outliers and resistance?Outliers and Changes to Data Sets: Compare how a changed extreme value affects mean and median.
When should I use append an observation?Outliers and Changes to Data Sets: Update both total and count when adding a value.