9709 · 5.1
Representation of data flashcards
Revision flashcards for Cambridge 9709 Representation of data (syllabus 5.1). Flip, recall, then mark a real past-paper question.
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What is a key difference between a histogram and a bar chart?
A histogram is for continuous data with no gaps between bars, and the area of each bar is proportional to frequency. A bar chart is for discrete or categorical data and has gaps between bars.
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What is the formula for Frequency Density?
Frequency Density = Frequency / Class Width. This is used as the vertical axis for a histogram with unequal class widths.
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What are class boundaries?
The exact values that separate one class from the next in grouped continuous data. For example, for classes 10-14 and 15-19, the boundary is 14.5.
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How do you find the mid-point of a class interval?
Add the upper and lower class boundaries and divide by 2. For a class 10 ≤ x < 20, the midpoint is (10 + 20) / 2 = 15.
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What is the formula for the estimated mean of grouped data?
$\bar{x} \approx \frac{\sum fx}{\sum f}$, where $x$ is the mid-point of each class and $f$ is the frequency of that class.
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What is a cumulative frequency graph also known as?
An ogive.
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How do you plot a cumulative frequency graph?
Plot the cumulative frequency on the y-axis against the upper class boundary of each class on the x-axis. The first point is (lower boundary of first class, 0).
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How do you estimate the median from a cumulative frequency graph?
Find the position of the (n/2)th value on the cumulative frequency axis, read across to the curve, and then read down to the horizontal axis.
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How do you find the Interquartile Range (IQR) from a cumulative frequency graph?
Find the values for the upper quartile (Q3 at 3n/4) and lower quartile (Q1 at n/4) from the graph. The IQR is Q3 - Q1.
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What are the five key values summarised in a box-and-whisker plot?
Minimum value, Lower Quartile (Q1), Median (Q2), Upper Quartile (Q3), and Maximum value.
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Common Trap: When calculating the mean from a grouped frequency table, what value must you use for 'x' in Σfx?
You must use the class mid-point. Using the lower/upper boundary or the class width is a common error.
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When comparing two datasets, what two features must you always comment on?
You must compare a measure of central tendency (e.g., median or mean) and a measure of spread (e.g., IQR or standard deviation).