Flashcards · J560 · Topic 12

Statistics flashcards

16 cards on Topic 12, subtopics 12.01 to 12.03. Pick a subtopic or study them all.

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Population compared with sample: Population: everything the study is about. Sample: a smaller group taken from it, used to estimate the population.
Simple random sample, and how to take one: Every member has an equal chance of selection. Number everyone in the sampling frame, generate random numbers in that range, select the matching members and skip repeats.
Sources of bias in a sample: Sampling at only one place or time; a sampling frame that misses people; volunteers only; leading questions. A very small sample is unreliable, which is a separate issue from bias.
How do you estimate a population figure from a sample?: Proportion in the sample × population size, and say it is an estimate. A larger unbiased sample is more reliable.

Pie chart: 24 pupils, 5 chose walking. What angle?: 360 ÷ 24 = 15° per pupil, so 5 × 15 = 75°. Check the angles add to 360°.
Bar chart compared with histogram: Bar chart: gaps, shows categories or single values, height = frequency. Histogram: no gaps, continuous grouped data, area = frequency.
Time series: trend and seasonal variation: Trend: the long-term direction (rising, falling, steady). Seasonal variation: a pattern that repeats over a fixed period, such as a peak in the same quarter each year.
Multiple bar chart compared with composite bar chart: Multiple: bars for each group side by side. Composite: parts stacked in one bar, each section = top edge − bottom edge.
Frequency densityHigher: Frequency ÷ class width; frequency = density × width. Example: 4 < x ≤ 10 with frequency 27 has density 27 ÷ 6 = 4.5.
Cumulative frequency graph: plotting and readingHigher: Plot running totals at the upper class boundary, starting at (lowest boundary, 0). Read the median at n/2, the lower quartile at n/4 and the upper quartile at 3n/4.

Mean, median, mode and range: Mean: total ÷ count. Median: the middle value in order, at position (n + 1)/2. Mode: the most common value. Range: largest − smallest.
When is the median a better average than the mean?: When the data contain extreme values or are skewed: an extreme value moves the mean a lot but the median little.
How do you estimate the mean from grouped data?: Multiply each class midpoint by its frequency, add the products, and divide by the total frequency. It is an estimate because the actual values are not known.
Interquartile range and box plotsHigher: IQR = Q3 − Q1, the spread of the middle half, not affected by extreme values. A box plot shows minimum, Q1, median, Q3 and maximum.
Correlation, causation, interpolation and extrapolation: Correlation alone does not show that one variable causes the other. Interpolation (inside the data range) is usually safer than extrapolation (beyond it).
How can a graph misrepresent data?: A vertical axis that does not start at zero, uneven scale steps, missing labels, bars of unequal width or 3D effects, pictogram icons of different sizes, or a selected time period.