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Difficulty: MediumData Representation and Charts

Match each data representation concept on the left with its corresponding mathematical formula or definition on the right.

  • Sector angle of a category in a pie chartCategory FrequencyTotal Frequency×360∘\frac{\text{Category Frequency}}{\text{Total Frequency}} \times 360^\circ
  • Height of a histogram bar for equal class intervalsFrequency of the class interval
  • Height of a histogram bar for unequal class intervalsClass FrequencyClass Width\frac{\text{Class Frequency}}{\text{Class Width}}
  • Upper class boundary of an interval a−ba - b (with unit gap of 11 between classes)b+0.5b + 0.5

Answer

Sector angle of a category in a pie chart matches Category FrequencyTotal Frequency×360∘\frac{\text{Category Frequency}}{\text{Total Frequency}} \times 360^\circ; Height of a histogram bar for equal class intervals matches Frequency of the class interval; Height of a histogram bar for unequal class intervals matches Class FrequencyClass Width\frac{\text{Class Frequency}}{\text{Class Width}}; Upper class boundary of an interval a−ba - b matches b+0.5b + 0.5.
Each chart concept matches its standard definition: pie chart sector angles are proportional parts of 360∘360^\circ; histogram heights equal class frequencies when widths are equal, but equal frequency density when widths are unequal; and class boundaries adjust discrete limits by half the gap width.

Step-by-Step Solution

1
Identify the formula for calculating pie chart sector angles.
Sector angle = Category FrequencyTotal Frequency×360∘\frac{\text{Category Frequency}}{\text{Total Frequency}} \times 360^\circ.
Pie charts distribute 360∘360^\circ proportionally according to the frequency of each category.
2
Determine histogram bar height representation under uniform class widths.
Bar height corresponds directly to the class frequency.
With uniform widths, the area of each rectangle is directly proportional to its height.
3
Determine histogram bar height representation under varying class widths.
Bar height corresponds to frequency density, calculated as Class FrequencyClass Width\frac{\text{Class Frequency}}{\text{Class Width}}.
To maintain area proportional to frequency across varying widths, height must equal frequency divided by width.
4
Determine upper class boundary for discrete class intervals.
Upper boundary = b+0.5b + 0.5.
Class boundaries eliminate gaps between discrete intervals by extending limits by half of the unit gap.

Key Concept

Data Representation Principles in Charts and Frequency Tables
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Topics

Data Representation and Charts

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