Flashcards · 0580 · Topic 9

Statistics flashcards

35 cards on Topic 9, subtopics 9.1 to 9.7. Pick a subtopic or study them all.

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9.1 Classifying statistical data

Qualitative and quantitative data: Qualitative (categorical): words or categories, e.g. favourite sport. Quantitative: numbers.
Discrete and continuous data: Discrete: counted, can only take certain values (e.g. number of siblings, goals scored). Continuous: measured, can take any value in a range (e.g. height, time).
Tally table: Each item is recorded as a stroke, grouped in fives. The frequency is the total for each row; the frequencies must add up to the number of data items.
How do you fill a missing cell in a two-way table?: Use the row and column totals: every row and every column must add up. E.g. girls total 16 and girls walk 5, so girls by bus = 16 − 5 = 11.
Classes 10 ≤ t < 15 and 15 ≤ t < 20: where does 15 go?: Only in 15 ≤ t < 20: the first class does not include 15.

9.2 Interpreting statistical data

How do you compare two sets of data?: Compare an average and a measure of spread, and say what each means in context (e.g. "Class Q did better on average; Class P’s marks were more consistent").
Restrictions on drawing conclusions from data: Is the sample big enough and representative? Is the time period long enough? Does the data measure what is claimed? A link between two quantities does not prove that one causes the other.
Two-way table: 38 members swim, 18 of them juniors; 80 members in all. What fraction of swimmers are juniors?: 18/38 = 9/19. The denominator is the swimming total, because the question is about swimmers.
Exam trap when comparing data sets: Comparing a median from one set with a mean from the other. Compare like with like, and comment on more than one feature.
Why is the interquartile range useful for comparing data sets?Extended: It measures the spread of the middle half of the data, so extreme values do not affect it. A smaller IQR means more consistent data.

9.3 Averages and range

Mean, median, mode and range: Mean: sum of the values ÷ number of values. Median: the middle value once in order. Mode: the most frequent value. Range: largest − smallest.
Find the mean, median, mode and range of 3, 5, 5, 7, 9, 20: Mean = 49/6 = 8.17 (3 s.f.) Median = (5 + 7)/2 = 6 Mode = 5 Range = 20 − 3 = 17
Which average to use: data with an extreme value, and non-numerical data: Extreme values (outliers): the median, which they do not affect. Non-numerical (categorical) data: the mode, the only average that works.
Mean from a frequency table: Multiply each value by its frequency, add these, then divide by the total frequency: Σ(x × f) ÷ Σf. E.g. a total of 26 pets for 20 students gives a mean of 1.3.
Estimating the mean of grouped dataExtended: Σ(midpoint × frequency) ÷ total frequency. It is an estimate because the midpoint stands in for the unknown values in each class.
Modal class and interquartile rangeExtended: Modal class: the class with the highest frequency in grouped data. Interquartile range = upper quartile − lower quartile: the spread of the middle 50%.

9.4 Statistical charts and diagrams

Pie chart: 12 of 40 people chose red. What angle is the red sector?: 12/40 × 360° = 108°. The angles must add up to 360°.
Composite (stacked) bar chart: a section runs from 60 to 90. What does it show?: 90 − 60 = 30. Each section is end minus start; reading off 90 is the classic error.
Dual or composite bar chart: which shows what best?: Dual (side by side): comparing one category across groups, as every bar starts at 0. Composite (stacked): comparing totals and the make-up of each total.
Stem-and-leaf diagram: what must it have?: Leaves in order along each row, and a key (e.g. 14 | 2 means 14.2). With 20 values, the median is halfway between the 10th and 11th.
Rules for drawing a bar chart: Label both axes, start the frequency axis at 0 with an even scale, make every bar the same width and leave equal gaps between bars for categories.
Two pie charts with different totals: does the bigger sector mean more people?: Not necessarily. A sector shows a proportion of its own total; compare actual numbers using each total.

9.5 Scatter diagrams

Positive, negative and zero correlation: Positive: as one variable increases the other tends to increase. Negative: as one increases the other tends to decrease. Zero: no clear pattern.
How do you draw a line of best fit?: One ruled straight line, drawn by eye, following the trend across the data, with the points roughly evenly spread either side. It need not pass through any data point or the origin.
When should you NOT draw a line of best fit?: When the scatter diagram shows zero correlation.
Using a line of best fit to estimate a value: Read across to the line and then down (or up and across). Estimates inside the range of the data are more reliable than those beyond it.

9.6 Cumulative frequency diagrams

How do you draw a cumulative frequency diagram?Extended: Find the running totals. Plot each one at the UPPER class boundary (not the midpoint), start at cumulative frequency 0, and join the points with a smooth curve.
Reading the median and quartiles from a cumulative frequency curve (total frequency n)Extended: Median: at cumulative frequency n/2. Lower quartile: n/4. Upper quartile: 3n/4. IQR = upper quartile − lower quartile. Start on the cumulative frequency axis.
n = 80. At what cumulative frequency do you read the 90th percentile?Extended: 0.9 × 80 = 72
120 students; the cumulative frequency at 40 minutes is 92. How many took more than 40 minutes?Extended: 120 − 92 = 28. For "more than", subtract from the total.
Exam trap: using (n + 1)/2 for the median on a cumulative frequency diagramExtended: (n + 1)/2 is for a list of individual values. On a cumulative frequency diagram, read the median at n/2.

9.7 Histograms

Frequency densityExtended: frequency density = frequency ÷ class width The vertical axis of a histogram is labelled "Frequency density".
Why use frequency density on a histogram?Extended: For classes of unequal width. Plotting raw frequency would make the wider classes look too big; with frequency density, the area of each bar shows its frequency.
Class 10 ≤ x < 15 has frequency 20; class 15 ≤ x < 25 has frequency 30. Find each frequency density.Extended: 20 ÷ 5 = 4 30 ÷ 10 = 3 The second class has more items but a lower bar, because it is wider.
A histogram bar has frequency density 2.4 and class width 5. Find the frequency.Extended: frequency = frequency density × class width = 2.4 × 5 = 12