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Exercises for Question Type 1: Constructing histograms given the frequency distribution table - IB | RevisionDojo

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Question Type 1: Constructing histograms given the frequency distribution table

Question Type 1: Constructing histograms given the frequency distribution table Exercises

Question 1

Skill question

The frequency distribution table below shows the number of students scoring marks in intervals of width 10: Class interval (marks): 0–10, 10–20, 20–30, 30–40 Frequency: 3, 7, 12, 8 Draw a histogram to represent this data.

Question 2

Skill question

A frequency table for test scores is given below. Add a column of relative frequencies. Class interval (score): 0–20, 20–40, 40–60, 60–80, 80–100 Frequency: 2, 8, 15, 10, 5

Question 3

Skill question

A histogram has three bars with the following class intervals and frequency densities: Class interval: 2–4, 4–9, 9–15 Density: 3, 2, 1 Using these, find the frequency for each class and complete the frequency distribution table.

Question 4

Skill question

The daily commute times (in minutes) of 40 employees are summarised in the table below: Class interval: 0–10, 10–20, 20–30, 30–60 Frequency: 4, 12, 15, 9 Add two new columns to this table: (i) cumulative frequency, (ii) class midpoint.

Question 5

Skill question

A histogram has bars of the following widths and heights (on a scale where the vertical axis measures frequency directly): Class interval: 0–2 (height 5), 2–6 (height 3), 6–10 (height 2) Complete the frequency distribution table by finding the frequency densities and frequencies.

Question 6

Skill question

The following frequency distribution has unequal class widths. Construct a histogram by first computing the frequency density for each class: Class interval: 0–5, 5–15, 15–30 Frequency: 4, 9, 7

Question 7

Skill question

The frequency distribution below gives heights (in cm) of a group of children: Class interval: 100–110, 110–130, 130–160 Frequency: 5, 12, 8 (a) Draw a histogram to represent the data. (b) From your histogram, state the modal class interval.

Question 8

Skill question

A histogram representing the ages of 120 participants has the following frequency distribution: Class interval (years): 10–20, 20–30, 30–40, 40–50 Frequency: 24, 36, 30, 30 Estimate the proportion of participants aged under 30.

Question 9

Skill question

The following raw data show the daily number of pages read by 12 students: 2, 7, 9, 5, 12, 8, 15, 3, 6, 11, 10, 4. Group the data into class intervals of width 5 starting at 0 (i.e. 0–5, 5–10, 10–15), then construct the corresponding frequency distribution table.

Question 10

Skill question

A histogram of exam scores shows that the bar for 70–80 has a greater height than the bar for 80–100, yet the frequency for 70–80 (8 students) is lower than that for 80–100 (12 students). Explain how this is possible.

Question 11

Skill question

A histogram with unequal class widths is to represent 50 observations. For class intervals 0–5, 5–20 and 20–50, the bars are drawn with heights (frequency densities) 1.2, 0.8 and $h$ respectively. If the total frequency is 50, find $h$ .