Frequency distribution and histograms

Lessons

• Introduction
  What is a frequency distribution? Why is it important?

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• 1.
  Constructing Frequency Distribution Table and Histograms
  Listed below are the heights of a class of $7^{th}$ graders:
  

  119	116	120	134	119	117	115
  122	125	124	128	122	135	126
  135	120	112	119	115	124	120
  117	123	140	125	130	113	128
  125	115	131	122	120	138	116

  
  
  
  a)

  Construct a frequency distribution table based on the data set above with the following information:
  1) class (set class width as 4 and lower limits of the classes as multiples of 4)
  2) frequency
  3) relative frequency
  4) cumulative frequency
  
  
  
  b)

  From the frequency distribution table in the previous part, construct a histogram. Use class midpoints on $x$-axis and frequency on $y$-axis.
  
  

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• 2.
  Interpreting Histograms
  Answer the questions based on the histogram below.
  
  
  
  
  a)

  How many days had more than 35.5 mm of rainfall?
  
  
  b)

  How many more days had 11.5 to 17.5 mm of rainfall than between 35.5 to 47.5 mm of rainfall?
  
  
  c)

  What is the relative frequency of having 17.5 to 23.5 mm of rainfall?
  
  

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• 3.
  The histogram below shows the average daily cholesterol intake of 40 people.
  
  
  
  
  a)

  What will change in the histogram if class midpoints are used on $x$-axis?
  
  
  b)

  What will change in the histogram if relative frequency is used on $y$-axis?
  
  
  c)

  What will change in the histogram if cumulative frequency is used on $y$-axis?
  
  
  d)

  What kind of interpretations can be made from the cumulative frequency histogram?
  
  

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