Statistics flashcards

Topic 6: Statistics

Random sample compared with biased sample

Random: every member of the population has an equal chance of being chosen. Biased: some members are more likely to be chosen, so results are skewed. A bigger random sample is more reliable.

Discrete compared with continuous data

Discrete: separate values, usually counts. Continuous: measured values that can take any value in a range.

How do you estimate the mean from grouped data?

1. Find each class midpoint. 2. Multiply each midpoint by its frequency and add. 3. Divide by the total frequency (not the number of classes). It is an estimate because the exact values are not known.

Position of the median

The (n + 1)/2 th value, with the data in order. In a frequency table, keep a running total until you pass that position.

Pie chart angle

Angle = (frequency ÷ total) × 360°. Check that the angles add up to 360°.

Frequency densityHigher

Frequency density = frequency ÷ class width. It goes on the vertical axis of a histogram; frequency = bar area. Example: 20 < t ≤ 40 with frequency 30 has density 30 ÷ 20 = 1.5.

Cumulative frequency graph: where are the points plotted, and how do you read the median?Higher

Plot each running total at the upper class boundary. Read the median across from n/2, the lower quartile from n/4 and the upper quartile from 3n/4.

Box plot and interquartile rangeHigher

A box plot shows minimum, LQ, median, UQ and maximum. IQR = UQ − LQ. The IQR is not affected by extreme values, so it is a better measure of spread than the range when there are outliers.

Scatter graphs: correlation, causation and extrapolation

Correlation does not mean one variable causes the other. Interpolation (inside the data) is fairly reliable; extrapolation (outside the data) may not be.

How do you compare two distributions?

Compare an average (such as the median or mean) and a measure of spread (the range), each in a sentence about the context.

Comparing two distributions with box plotsHigher

Compare the medians (average) and the interquartile ranges (spread), each in a sentence about the context. A smaller IQR means the middle half of the data is more consistent.