Flashcards · 4040 · Topic 2

Summary representation of data flashcards

19 cards on Topic 2, subtopics 2.1 to 2.4. Pick a subtopic or study them all.

Study mode needs JavaScript. Every card is listed below, so you can still cover the answers and test yourself.

All 19 cards

For a quick read-through or printing. Cover the right-hand side to test yourself.

What rules must the categories of a frequency table follow?: They must not overlap and must cover every observation. Tally in fives, then check that the frequencies add to the number of observations.
How do you find a missing entry in a two-way table?: Subtract from a row or column total, then check it the other way using the other direction. Row totals, column totals and the grand total must all agree.
In a two-way table, 25 of the 36 Year 11 pupils walk. What percentage of Year 11 walk?: 25 ÷ 36 × 100 = 69.4% (1 d.p.). The base is the Year 11 row total, not the grand total.
What is the difference between a frequency table and a two-way table?: A frequency table classifies data by one variable. A two-way table cross-classifies by two variables at once.

How do you read a frequency from a pie chart?: Frequency = (angle ÷ 360) × total. Example: a 135° sector in a pie chart of 80 people → 135 ÷ 360 × 80 = 30 people.
A pie chart with total 40 has radius 3 cm. Find the radius for total 90, with areas in proportion to totals: Radius = 3 × √(90 ÷ 40) = 3 × 1.5 = 4.5 cm. The radii are in the ratio of the square roots of the totals, not the totals.
A pictogram uses 1 symbol = 4 items. How many symbols show 22 items?: 22 ÷ 4 = 5½ symbols. Give a key, draw symbols the same size, and use whole and half symbols only.
What is the difference between a sectional and a percentage bar chart?: A sectional bar shows amounts: its height is the total. A percentage bar shows shares: every bar is the same height (100%), so groups with different totals can be compared.
In a group of 30, n(A) = 14, n(B) = 11 and n(A ∩ B) = 5. How many are in neither set?: n(A ∪ B) = 14 + 11 − 5 = 20, so neither = 30 − 20 = 10. A only = 9, B only = 6.
What are the rules for drawing a stem-and-leaf diagram?: Stems in order with none missing, leaves in order and equally spaced, and a key with units (for example 3 | 4 means 3.4 kg). In a back-to-back diagram the leaves are ordered outwards from the stem on both sides.

What is a Venn diagram good for, and what is its drawback?: It shows overlaps and the "neither" group, with counts at a glance. It becomes hard to read with many sets and shows counts only.
What are the advantages and disadvantages of a stem-and-leaf diagram?: No data is lost and the shape is visible. It becomes long and unwieldy for a large data set. A back-to-back version compares only two sets.
What are the advantages and disadvantages of a box-and-whisker diagram?: It is quick to read, works for any size of data set and compares median and spread directly. The individual values are lost and it does not show the mean.
Pie chart or bar chart: what is the trade-off?: A pie chart shows proportion clearly, but it is harder than a bar chart for comparing precise values across categories.
When should you use a comparative pie chart or a dual bar chart rather than a single chart?: When the question needs two or more data sets compared, not just one data set displayed.

What should a comparison of two data sets include?: One average (such as the median), one measure of spread (IQR or range), a sentence in context using comparison words, and a conclusion that answers the question.
Two classes both have median 64. Class 1 has IQR 14 and Class 2 has IQR 24. Compare them: The typical pupil did equally well in both classes (same median). Class 1 is more consistent, because its IQR is smaller.
Club X has 60 of 240 members in a quiz; Club Y has 24 of 80. Which has the higher participation?: X: 60 ÷ 240 = 25%. Y: 24 ÷ 80 = 30%. Club Y has the higher rate, though Club X has the larger number. With groups of different sizes, compare percentages.
In a sectional bar chart (1 cm = 10 units), parts end at 4 cm and 6.5 cm. What is the second part?: (6.5 − 4) × 10 = 25 units. Subtract the lower boundary from the upper one; do not read 6.5 cm as the part on its own.