Flashcards · 4040 · Topic 3

Formation of data into ungrouped or grouped frequency distributions flashcards

12 cards on Topic 3, subtopics 3.1 to 3.2. Pick a subtopic or study them all.

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What is the difference between class limits and class boundaries?: Limits are the lowest and highest values that can be written in a class, as printed; there are gaps between classes. Boundaries are the exact edges on the number line, so neighbouring classes meet.
Masses are recorded to the nearest kg. Find the boundaries, width and mid-point of the class 40–44: Gap 1, half-gap 0.5. Boundaries 39.5 and 44.5. Width 44.5 − 39.5 = 5. Mid-point (39.5 + 44.5) ÷ 2 = 42.
Lengths are recorded to 1 decimal place. What are the boundaries of the class 2.0–2.4?: Gap 0.1, so half-gap 0.05. Boundaries 1.95 and 2.45; width 0.5; mid-point 2.2.
What are the boundaries of the class 135 ≤ h < 145?: Exactly 135 and 145: an inequality class is already in boundary form and needs no adjustment. Width 10, mid-point 140.
Ages are recorded as age last birthday. What are the width and mid-point of the class 10–14?: The class covers ages from 10 up to, but not including, 15. Width 5, mid-point 12.5 (not 12).
What is the classic error when finding the width of a class such as 40–44?: Taking upper limit − lower limit, which gives 4. The width is upper boundary − lower boundary = 5.

How do you draw a frequency polygon?: Plot (midpoint, frequency) for each class, plus a zero-frequency point at the midpoint of an empty class before the first and after the last. Join with straight ruled lines.
Classes run 20–<30 up to 60–<70. Where are the zero points of the frequency polygon?: At x = 15 and x = 75, the midpoints of the empty classes 10–<20 and 70–<80.
How is a histogram with unequal class widths drawn?: Find each width from the boundaries, then frequency density = frequency ÷ width. Draw touching bars from boundary to boundary at that height, and label the axis "frequency density". The area of each bar is its frequency.
A histogram bar of width 20 has frequency density 0.65. What frequency does it show?: Frequency = density × width = 0.65 × 20 = 13.
The class 10 ≤ x < 20 has frequency 30. Estimate how many values lie between 10 and 14: Assuming an even spread: density 30 ÷ 10 = 3, so 3 × 4 = 12. It is an estimate.
What is the modal class on a histogram with unequal widths?: The class with the greatest frequency density, which is not necessarily the class with the greatest frequency.