Statistics and Probability
Statistics
Be able to read and draw bar charts, pie charts, line graphs, histograms and scatter diagrams. For pie charts, each category's angle = (frequency / total) x 360 degrees. Know the averages: mean = total / number of values; median = middle value when ordered (average the two middle values if n is even); mode = most frequent; range = largest - smallest. For frequency tables use the total of frequency x value; for grouped data use class midpoints and identify the modal class and the interval containing the median. Cumulative frequency curves give the median and quartiles at one half, one quarter and three quarters of the total. Describe correlation as positive, negative or none, and distinguish it from causation.
Probability
Use P(A) = favourable outcomes / total equally likely outcomes, with 0 <= P <= 1 and P(not A) = 1 - P(A). For mutually exclusive events add probabilities; for independent events multiply. Draw tree diagrams for two-stage experiments and remember that without replacement changes the denominators and numerators on the second branch. Use at least one = 1 - P(none). Expected frequency = probability x number of trials.
Traps
- Using the wrong total, especially when a table has a total row.
- Forgetting to order the data before finding the median.
- Class boundaries: the class 10 to 19 has midpoint 14.5, not 14.
- With no replacement, the second probability uses the reduced total.
- Pie-chart angles must add to 360 degrees.
Rule of thumb
List the sample space or draw the tree before calculating, and write each probability as a fraction of the remaining total.
Example: 3 red and 5 blue counters; two drawn without replacement: P(both red) = 3/8 x 2/7 = 3/28.