Study guide: Ask Statistical Questions and Summarize Distributions
Recognize variability, display data, measure center, and compare spread with IQR and MAD.
Ideas to explain in your own words
- A statistical question expects multiple observations with possible variation, such as how long several supplied tasks take.
- The mean redistributes the total equally over all observations.
- Quartiles split ordered data into lower and upper portions.
- Mean absolute deviation averages the distances from the mean.
Useful vocabulary
- median
- The middle value of ordered data, or the mean of the two middle values.
- interquartile range
- The difference between upper and lower quartiles.
- mean absolute deviation
- The mean distance of data values from their mean.
Watch your reasoning
- Histogram bins must give each observation exactly one home.
- The median requires sorted data; the mean need not be a value present in the record.
- IQR is Q3 minus Q1, not maximum minus minimum.
- A shared mean does not imply equal spread or identical distributions.
A worked review example
Times are 2,3,3,5,7 minutes. Asking how these task times vary is statistical. A dot plot has one mark at two, two at three, one at five, and one at seven. With bins [0,4) and [4,8), counts are three and two; four belongs only in the second bin. Specify what was observed and its measurement unit. Histogram bins must give each observation exactly one home. Write the question, measurement unit, and explicit interval boundaries above the display.
Make a practice plan
- Ask Questions That Anticipate Variation: Plot 1,1,4,6,6,7 and use bins [0,4),[4,8). Expected: six marks; bin counts 2 and 4.
- Compare Mean and Median as Centers: For 1,2,3,4,20, mean is six and median three. Explain the influence of twenty.
- Use Quartiles and Interquartile Range: For 2,3,4,5,9,10,11,12, Q1=3.5,Q3=10.5,IQR=7,median=7.
- Use Mean Absolute Deviation to Compare Spread: Compare 1,1,9,9 and 4,4,6,6. Expected mean five for both; MAD four versus one.