Flashcards · 4024 · Topic 9

Statistics flashcards

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

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Categorical data: Data described in words, for example colour or type of transport.
Discrete data: Numerical data that can take only separate values, for example number of goals or shoe size.
Continuous data: Numerical data that can take any value in a range, for example time, mass or length.
How do you fill in a missing entry in a two-way table?: 1. Find a row or column with only one blank. 2. Subtract the known entries from its total. 3. Repeat until the table is full. 4. Check the grand total both across and down.

How do you compare two sets of data?: Make one comparison of an average and one of the spread, each in context and quoting figures from the data.
Two classes have the same mean mark. Class A has range 8 and Class B range 35. What does this tell you?: The typical marks are the same, but Class A is more consistent; the marks in Class B are more spread out.
Give reasons a conclusion from data may not be reliable: The sample is small or biased; grouping hides detail; averages hide spread; a chart does not prove cause; scales can mislead; predictions beyond the data are unreliable.

Mean, median, mode and range: Mean: sum of values ÷ number of values. Median: middle value of the ordered data. Mode: most common value. Range: largest − smallest.
Position of the median of n ordered values: (n + 1) ÷ 2. For 20 values this is 10.5, so the median is halfway between the 10th and 11th values.
Mean from a frequency table: x = 0, 1, 2, 3 with frequencies 5, 7, 6, 2: Mean = Σfx ÷ Σf Σfx = 0 + 7 + 12 + 6 = 25, Σf = 20 Mean = 25 ÷ 20 = 1.25
How do you estimate the mean of grouped data?: 1. Find the midpoint of each class. 2. Multiply each frequency by its midpoint. 3. Divide the total of these by the total frequency. It is an estimate because the exact values are not known.
Which average should you use when the data has an outlier?: The median. The mean is pulled towards an extreme value; the median is hardly affected.

Pie chart: angle for a category: Angle = (frequency ÷ total) × 360°. Example: 14 out of 40 gives 14/40 × 360° = 126°. Check the angles add up to 360°.
A pie chart shows 117 people. How many does an 80° sector represent?: Frequency = (angle ÷ 360°) × total = 80/360 × 117 = 26 people.
Composite bar chart and dual bar chart: Composite: parts stacked on one bar; the bar height is the total. Read a section as its top minus its bottom. Dual: two bars side by side for each category, to compare the groups.
Bar chart: what should it show?: Bars of equal width with gaps between them, a scale starting from zero, and labelled axes.

Positive, negative and zero correlation: Positive: as x increases, y tends to increase. Negative: as x increases, y tends to decrease. Zero: no link. Strong means the points lie close to a line.
How do you draw a line of best fit?: Plot the mean point of the two variables. Draw a single ruled line through or near it, with the points roughly evenly spread on both sides along the whole line.
Does correlation show that one variable causes the other?: No. Correlation shows a link in the data, not cause and effect.
When is an estimate from a line of best fit reliable?: Inside the range of the data (interpolation). Far outside the range (extrapolation) it is unreliable.
A line of best fit passes through (10, 25) and (30, 65). Find its equation.: Gradient = (65 − 25) ÷ (30 − 10) = 2. c = 25 − 2 × 10 = 5, so y = 2x + 5.

Where do you plot the points of a cumulative frequency diagram?: At the upper class boundary of each class, against the running total. Also plot (lower boundary of the first class, 0).
How do you join the points of a cumulative frequency diagram?: With a smooth curve (not a ruled line). It never slopes downwards, because frequencies cannot be negative.
n = 240. At what heights do you read the lower quartile, median and upper quartile?: n/4 = 60 (lower quartile), n/2 = 120 (median), 3n/4 = 180 (upper quartile). Read across to the curve, then down to the axis.
Interquartile range: IQR = upper quartile − lower quartile. It measures the spread of the middle half of the data.
Cumulative frequency: how many values are more than x?: Read the cumulative frequency at x (the number at or below x) and subtract it from the total n.

Frequency density: Frequency density = frequency ÷ class width. It is the height of a histogram bar, and the vertical axis is labelled "Frequency density".
In a histogram, what does the area of a bar show?: The frequency: frequency = frequency density × class width. Bars touch, with no gaps.
The class 2 ≤ x < 8 has frequency 9. Find the bar height.: Width = 8 − 2 = 6. Frequency density = 9 ÷ 6 = 1.5.
A bar from 30 to 45 has height 0.8. How many values does it represent?: Width = 15. Frequency = 15 × 0.8 = 12.
Which class of a histogram holds the most values?: The bar with the largest area, not necessarily the tallest bar.
A bar from 40 to 60 has height 1.5. Estimate how many values lie from 50 to 60.: 10 × 1.5 = 15, assuming the values are spread evenly through the class. State that assumption.