2. Data Analysis (D)
  3. Lesson 5: Interpreting Histograms

Exercises


  1. Which of the following can be read directly from a histogram?
    1. Data type
    2. Frequency of each interval
    3. Raw data
    4. Mean of the data
    5. Most frequent interval
    6. Approximate minimum and maximum data values
    7. Least frequent interval
    8. Range of the data
  2. Examine the following histogram and answer the questions below.
    The information shown in this histogram can be found in the Alternative Format for Question 2.

    Number of Books Read in March

    Number of Books Read Number of People
    \(0\) – \(2\) \(11\)
    \(2\) – \(4\) \(10\)
    \(4\) – \(6\) \(13\)
    \(6\) – \(8\) \(3\)
    \(8\) – \(10\) \(2\)
    \(10\) – \(12\) \(1\)
    1. What type of data is displayed?
    2. What is the most frequent interval?
    3. How many people were surveyed in total?
    4. How many people read at least \(6\) but less than \(8\) books?
    5. What percentage of people read at least \(8\) but less than \(10\) books?
  3. What are some advantages of histograms? What are some limitations of histograms?
  4. Histograms have been created to compare your cooking with your friend's cooking on the same graph.
    Which set of histograms would you not use if your goal was to show that more people prefer your cooking to your friend's cooking?

    Favourite Cook — You

    Age of Voter Number of Votes
    \(6\) – \(10\) \(9\)
    \(11\) – \(15\) \(6\)
    \(16\) – \(20\) \(12\)
    \(21\) – \(25\) \(12\)
    \(26\) – \(30\) \(8\)
    \(31\) – \(35\) \(15\)

    Favourite Cook — Your Friend

    Age of Voter Number of Votes
    \(6\) – \(10\) \(8\)
    \(11\) – \(15\) \(8\)
    \(16\) – \(20\) \(12\)
    \(21\) – \(25\) \(12\)
    \(26\) – \(30\) \(14\)
    \(31\) – \(35\) \(1\)
    1. The histogram is divided into 5, 5-year intervals. Some age demographics prefer you as a cook, some prefer your friend.
    2. The histogram is divided into 2, 15-year intervals. Ages 5 to 20 slightly prefer your friend as cook, ages 20 to 35 prefer you.
    3. This histogram has the same age intervals but the y-axis scale goes up to 200, making it difficult to differentiate the height of the bars.
  5. The daily high temperatures on the 5th, 10th, 15th, 20th, and 25th of each month were measured during the course of one year in a particular city. The following raw data collected is to be displayed in a graph. You would like to argue that there is a need to install air conditioners in the schools in the city.

    Daily High Temperatures (\({}^{\circ}\)C)

    Month 5th 10th 15th 20th 25th
    January \(8\) \(-3\) \(-6\) \(1\) \(0\)
    February \(-2\) \(-7\) \(1\) \( 1\) \(3\)
    March \(-12\) \(-2\) \(-10\) \(2\) \(4\)
    April \(6\) \(10\) \(8\) \(8\) \(8\)
    May \(10\) \(10\) \(20\) \(25\) \(23\)
    June \(16\) \(29\) \(20\) \(28\) \(26\)
    July \(27\) \(24\) \(27\) \(26\) \(23\)
    August \(23\) \(27\) \(27\) \(27\) \(22\)
    September \(23\) \(19\) \(26\) \(25\) \(31\)
    October \(27\) \(22\) \(24\) \(22\) \(12\)
    November \(17\) \(-8\) \(6\) \(5\) \(10\)
    December \(12\) \(-4\) \(-10\) \(0\) \(-5\)
    1. This data could be displayed in a line graph or a histogram. Which type of graph would you use in order to make your argument the most convincing? Explain.
    2. Create three histograms with the following interval choices.
      1. Two intervals, starting at \(-12^\circ\) and ending at \(34^\circ\).
      2. Nine intervals, starting at \(-12^\circ\) and ending at \(33^\circ\).
      3. Four intervals, starting at \(-12^\circ\) and ending at \(32^\circ\).
      Which choice of intervals do you think produces the histogram that provides the most convincing argument? 
  6. Consider the following histogram showing the heights of all Grade 7 and 8 students in Mathopolis school.
    The information shown in this histogram can be found in the Alternative Format for Question 6.

    Heights of Grade 7 and Grade 8 Students

    Height (in cm) Number of Students
    \(135\) – \(140\) \(1\)
    \(140\) – \(145\) \(9\)
    \(145\) – \(150\) \(44\)
    \(150\) – \(155\) \(20\)
    \(155\) – \(160\) \(5\)
    \(160\) – \(165\) \(1\)
    Based on the information in this histogram, answer the following questions or explain why you cannot determine the answer from the histogram.
    1. What is the minimum possible height range of Grade 7 and 8 students at the school?
    2. What is the maximum possible height range of Grade 7 and 8 students at the school?
    3. What is the median height of Grade 7 and 8 students at the school?
    4. What percentage of students are taller than \(150\) cm?
    5. What grade had the tallest students?
  7. The maximum daily wind speeds were measured in St. John's, NL and Victoria, BC in February 2018.
    1. The data collected is displayed in the following two histograms. What conclusions can be drawn from these histograms? Explain.
      The information shown in this histogram can be found in the Alternative Format for Question 7.The information shown in this histogram can be found in the Alternative Format for Question 7.

      Daily Wind Speeds in St John's, NL

      Maximum Wind Speed (km/h) Number of Days
      \(25\) – \(35\) \(6\)
      \(35\) – \(45\) \(8\)
      \(45\) – \(55\) \(7\)
      \(55\) – \(65\) \(7\)
      \(65\) – \(75\) \(0\)

      Daily Wind Speeds in Victoria, BC

      Maximum Wind Speed (km/h) Number of Days
      \(0\) – \(11\) \(0\)
      \(11\) – \(22\) \(11\)
      \(22\) – \(33\) \(13\)
      \(33\) – \(44\) \(3\)
      \(44\) – \(55\) \(1\)
    2. Below is the raw data used to form the histograms in part a).
      City Maximum Wind Speeds
      St. John's, NL \(26\), \(49\), \(28\), \(44\), \(34\), \(46\), \(53\), \(43\), \(27\), \(29\),
      \( 41\), \( 55\), \(44\), \(40\), \(57\), \(58\), \(63\), \(48\), \(36\), \(26\),
      \(57\), \(37\), \(47\), \(58\), \(37\), \(58\), \(49\), \(51\)
      Victoria, BC \(51\), \( 21\), \( 21\), \( 26\), \( 33\), \( 29\), \( 21\), \( 16\), \( 18\), \( 31\),
      \( 40\), \( 42\), \( 21\), \( 13\), \( 27\), \( 18\), \( 29\), \( 22\), \( 22\), \( 18\),
      \( 26\), \( 29\), \( 26\), \( 17\), \( 25\), \( 29\), \( 32\), \( 16\)
      Does this raw data make you rethink any of your conclusions from part a)? Explain.
  8. Describe the mean of the underlying data in the histogram from Question 6 as best you can. Explain why your description is as accurate as possible.