Worksheet: Frequency Density and Histograms

In this worksheet, we will practice calculating frequency density and plotting histograms.

Q1:

The frequency table below gives the heights of a group of students.

Height, (Centimeters)150<153153<156156<157157<162162<165
Frequency60453010045

Which of the following histograms represents the given data?

  • A
  • B
  • C
  • D
  • ENone of the above

Q2:

The frequency table provided shows the ages of teenagers in a neighborhood.

Age, 𝑎 (Years)13<𝑎1414<𝑎1717<𝑎19
Frequency212410
Frequency Density218

Find the missing density from the table.

Q3:

The given histogram shows the ages of students in a school.

Which of the following frequency tables matches the histogram?

  • A
    Age, 𝑎 (Years) 9<𝑎1010<𝑎1212<𝑎1414<𝑎1717<𝑎1919<𝑎20
    Frequency46432.51
  • B
    Age, 𝑎 (Years) 8<𝑎1010<𝑎1212<𝑎1414<𝑎1717<𝑎1919<𝑎20
    Frequency4128951
  • C
    Age, 𝑎 (Years) 9<𝑎1010<𝑎1212<𝑎1414<𝑎1717<𝑎1919<𝑎20
    Frequency4128951
  • D
    Age, 𝑎 (Years) 9<𝑎1010<𝑎1212<𝑎1414<𝑎1616<𝑎1919<𝑎20
    Frequency4128951
  • E
    Age, 𝑎 (Years) 9<𝑎1010<𝑎1212<𝑎1414<𝑎1717<𝑎20
    Frequency412895

Q4:

The following table represents the speed of the members of a cycling club over a long-distance race.

Speed, 𝑠 (mph)5<𝑠88<𝑠1010<𝑠1515<𝑠2020<𝑠3030<𝑠35
Frequency12243520105

David drew a histogram to represent this data.

What is the mistake in this histogram?

  • AThe bar of the interval 30<𝑠35 represents the frequency instead of the frequency density.
  • BThe last interval should end at 36.
  • CThe bar of the interval 20<𝑠30 represents the frequency instead of the frequency density.
  • DNone of the bars represent the correct frequencies.
  • EThe intervals should be equal.

Q5:

The frequency table below represents the times students take to walk to school.

Time, 𝑡 (Minutes)0<𝑡44<𝑡88<𝑡1212<𝑡16
Frequency412168

Find the frequency density for each frequency class.

  • A1, 3, 4, 2
  • B4, 16, 32, 40
  • C1, 2, 3, 4
  • D0.8, 2.4, 3.2, 1.6
  • E2, 6, 8, 4

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