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Statistical Diagrams

Statistics

Bar charts

  • A bar chart shows discrete or categorical data, with the categories along the bottom and the frequency up the side
  • Bars are drawn with equal widths and with gaps between them, which is what distinguishes a bar chart from a histogram
  • The tallest bar gives the mode
  • The syllabus names two variants
    • A dual bar chart puts the bars for two data sets side by side for each category
    • A composite or stacked bar chart puts one on top of the other, so the total height is the combined frequency
A dual bar chart of the number of pets owned, with a pink Year 7 bar and a purple Year 8 bar side by side above each category from 0 to 5 pets, and a key underneath saying which colour is which
Source: Bar charts & pictograms by Save My Exams
  • When drawing one, pick a scale from the largest frequency so that it fits the space given
A bar chart of shoe sizes in a class, with shoe size along the bottom from 6 to 12 and frequency up the side: equal-width bars separated by gaps, the tallest at size 10 with a frequency of 11, which makes size 10 the mode
Source: Bar charts & pictograms by Save My Exams

Pictograms

  • A pictogram replaces bars with symbols, and a key states how many one whole symbol represents
  • Part-symbols show part-values, so with a key of one symbol representing 4 people, three and a half symbols means 14
  • Read the key before anything else, since the same picture means different amounts on different questions
A pictogram of the same shoe-size data drawn with boot symbols, one boot standing for 2 students as the key says, so a column of five and a half boots at size 10 means 11 students and a half boot means 1
Source: Bar charts & pictograms by Save My Exams
  • Choose an easy symbol to draw and halve if you are asked to make one
Exam tip

A pictogram is unreadable without its key, and part-symbols are read against it, so a half symbol against a key of 10 is 5. On a bar chart the bars are equal in width with gaps between them — the gaps are what distinguish it from a histogram, where the bars touch and the widths may differ.

Worked example

Reading a pictogram

On a pictogram of books read, one book symbol represents 10 books. March shows 3 whole symbols and one half symbol. April shows 5 whole symbols. How many books were read in each month, and how many more in April?

Solution:

  • Read the key first: every whole symbol stands for 10 books, so a half symbol stands for 5
  • March: 3 × 10 = 30, plus the half symbol worth 5
  • March = 35 books
  • April: 5 × 10 = 50 books
  • Difference = 50 − 35 = 15 more books in April
  • Counting symbols instead of reading the key would have given 3.5 and 5, which are not numbers of books at all