Cumulative Frequency DiagramsEdexcel IGCSE Maths: Flashcards

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What does 'cumulative frequency' mean?

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What does 'cumulative frequency' mean?: The running total of frequencies up to and including a given class interval.
When plotting a cumulative frequency graph, which value do you plot on the $x$ -axis for each class interval?: The upper bound (upper class boundary) of the interval — never the midpoint.
What shape should a cumulative frequency curve be?: A smooth, non-decreasing S-shaped curve called an ogive.
At what position on the cumulative frequency axis do you read off the median, for $n$ items of data?: $\frac{n}{2}$
At what position do you read off the lower quartile $Q_1$ ?: $\frac{n}{4}$
At what position do you read off the upper quartile $Q_3$ ?: $\frac{3n}{4}$
What is the formula for the interquartile range (IQR)?: $IQR = Q_3 - Q_1$
Why is the IQR often preferred over the range as a measure of spread?: Because the IQR is based on the middle 50% of the data, so it is less affected by extreme values or outliers.
What five values are shown on a box plot?: Minimum, lower quartile ( $Q_1$ ), median, upper quartile ( $Q_3$ ), and maximum.
What does the 'box' in a box plot represent?: The interquartile range — from $Q_1$ to $Q_3$ , with a line marking the median.
What do the 'whiskers' on a box plot represent?: Lines extending from the box out to the minimum and maximum data values.
When comparing two distributions, what two types of comment must you always make?: One comment on a measure of location (usually the median) and one comment on a measure of spread (usually the IQR or range), both written in context.
Should values read from a cumulative frequency graph be stated as exact or estimated?: Estimated — all readings taken from a graph are approximations, not exact values.
If $n = 60$ , at what cumulative frequency value do you find the median?: 30 (since $\frac{60}{2} = 30$ ).
What common plotting mistake do students make when drawing cumulative frequency graphs?: Plotting against the midpoint of the class interval instead of the upper bound.