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

Question 1

Skill question

Construct a histogram for the data by computing the frequency density for each class.

Data (length in cm):

Class interval	Frequency
0–10	8
10–20	12
20–30	20
30–50	10

State the frequency density (bar height) for each class.

Question 2

Skill question

A data set of ages (years) is grouped as follows. Compute the frequency densities to construct the histogram.

Class interval	Frequency
0–5	5
5–10	9
10–15	15
15–25	12

Give the frequency density for each class.

Question 3

Skill question

A histogram has bars with the following class intervals and frequency-density heights. Construct the frequency distribution table by computing the frequency in each class.

Class interval	Frequency density
0–5	1.2
5–10	2.0
10–20	0.8

Fill in the frequency for each class.

Question 4

Skill question

Construct the histogram by calculating the frequency density for each class.

Data (mass in kg):

Class interval	Frequency
50–55	6
55–60	9
60–70	20
70–90	15

Give the frequency density for each class.

Question 5

Skill question

From the histogram information below, complete the frequency table.

Class interval	Frequency density
40–50	1.5
50–60	2.1
60–80	0.9
80–100	0.6

Compute the frequency in each class.

Question 6

Skill question

Compute the frequency density for each class and hence specify the bar heights for the histogram.

Data (time in minutes):

Class interval	Frequency
0–5	4
5–8	7
8–12	12
12–20	9

Provide the list of frequency densities.

Question 7

Skill question

For the grouped data below, calculate the frequency density for each class to construct the histogram.

Data (speed in km/h):

Class interval	Frequency
40–50	16
50–52	8
52–60	24
60–80	12

State the frequency density for each class.

Question 8

Skill question

A histogram shows the following classes and bar heights (frequency densities). The total frequency is $N=120$ . Find the missing bar height and complete the frequencies.

Class interval	Frequency density
0–10	1.0
10–20	2.5
20–40	0.75
40–50	?

Compute the missing density and all class frequencies.

Question 9

Skill question

You will draw a histogram with vertical axis scaled so that 1 grid unit represents $0.5$ frequency-density units. Compute the frequency density and the actual bar height (in grid units) for each class.

Data (reaction time in s):

Class interval	Frequency
0.0–0.2	5
0.2–0.5	18
0.5–0.8	12
0.8–1.4	9

Report both the frequency density and the bar height for each class.

Question 10

Skill question

A histogram is summarized by class intervals and frequency densities. Also given is the total frequency $N=60$ . Complete the frequency table and verify the total.

Class interval	Frequency density
0–4	1.0
4–6	3.0
6–10	1.25
10–12	2.5

Find the frequency in each class and check that they sum to $N$ .

Question 11

Skill question

The histogram below is summarized by class widths and bar heights (frequency densities). Reconstruct the frequency table.

Class interval	Width	Frequency density
2.0–2.4	0.4	8.0
2.4–3.0	0.6	6.5
3.0–3.2	0.2	20.0
3.2–4.0	0.8	3.75

Find the frequency in each class.

Question 12

Skill question

A histogram uses a vertical axis labeled $k\times\text{frequency density}$ (i.e., heights are scaled by a constant $k$ ). The classes and plotted heights are as follows. If the actual frequency in $20$ – $30$ is $24$ , determine $k$ and reconstruct all class frequencies.

Class interval	Width	Plotted height ( $k\times$ density)
10–20	10	1.5
20–30	10	2.4
30–50	20	0.9
50–70	20	0.6

Find $k$ and the frequency in each class.

Question 13

Skill question

One class width in a histogram is unknown. The table shows class intervals (one with unknown upper bound), bar heights (frequency densities), and one known frequency. Find the missing class boundary and complete the frequencies.

Class interval	Frequency density	Frequency
0–5	1.4	?
5–?	2.0	18
?–20	0.8	?

Assume the three classes are contiguous with no gaps. Determine the missing upper bound and all three class frequencies.

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