Frequency distributions flashcards

Topic 3: Frequency distributions

What is gained and lost by grouping data into classes?

Grouping makes a large data set easier to summarise and compare, but the exact values are lost, so later results can only be estimates.

Which class measures are needed for discrete data and for continuous data?

Discrete: class limits, boundaries, midpoints and widths. Continuous: boundaries, midpoints and widths only, because the stated limits and the boundaries coincide.

A time is recorded as 9.7 s to 1 decimal place. Between which values does it lie?

9.65 ≤ t < 9.75. The lower bound uses ≤ and the upper bound uses <, so neighbouring classes never overlap.

Why must class intervals not overlap?

With classes such as 10–20 and 20–30, the value 20 could go in either class. Every value must belong to exactly one class.

What is frequency density, and when do you need it?

Frequency density = frequency ÷ class width. It goes on the vertical axis of a histogram with unequal class widths. Example: class 10 to under 30 (width 20) with frequency 8 → 0.4.

In a histogram, what represents the frequency of a class?

The area of its bar, not its height. This matters when the class widths are unequal.

How do you draw a frequency polygon?

Plot each frequency against the class midpoint and join the points with straight lines. It is used with equal class widths, and is the clearest way to compare two distributions on the same axes.

What is cumulative frequency, and where is it plotted?

The running total of the frequencies up to and including each class. It is plotted against the upper class boundaries, starting at the first lower boundary with 0.

How do you get an ordinary frequency table back from a cumulative one?

Subtract each cumulative total from the next one. The first class keeps its own cumulative total.

A cumulative frequency curve for 60 students passes through (50, 45). How many scored more than 50?

45 scored 50 or below, so 60 − 45 = 15 scored more than 50. Check whether the question asks for "below" or "above" before reading off the curve.