- Year 11
Moving between tables and histograms
I can construct a table from a histogram.
Lesson details
Key learning points
- A frequency table can be used to construct a histogram
- A histogram can be used to construct a frequency table
- Data is sometimes collected using uneven class widths
Keywords
Continuous data - Continuous data can take any value within a range. (Height, mass, temperature)
Histogram - A histogram is a diagram consisting of rectangles whose area is proportional to the frequency in each class and whose width is equal to the class interval.
Frequency density - Frequency density is proportional to the frequency per unit for the data in each class. Often, the multiplier is 1 meaning that frequency density = frequency ÷ class width.
Common misconception
Histograms with unequal bar widths are plotted against the frequency and/or pupils read the frequency density as the frequency of the class width.
Show what a histogram with unequal bar widths looks like when plotted against frequency. This visual aid will show pupils the distribution of data is difficult to see.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Frequency density is proportional to the frequency per unit for the data in each class. Often, the multiplier is 1 meaning...
Q2.Select which statements are true.
Q3.Here is some data on the masses of parcels. Which class interval shows a frequency density of 2?
Q4.Here is some data on the lengths of some string. Which class interval shows a frequency density of 1.4?
Q5.The histogram shows the masses of different parcels. How many parcels have a mass between 5 and 15 kg?
Q6.Select which of the following statements are true given a histogram with unequal bar widths plotted against frequency density.
Assessment exit quiz
6 Questions
Q1.Which of the following shows the frequency in a histogram with unequal bar widths?
Q2.Here are the times taken to type the alphabet. Match the class intervals with the correct frequency density.
$$0 < t \leq 10$$ - Frequency density = 0.4
$$10 < t \leq 15$$ - Frequency density = 1.6
$$15 < t \leq 20$$ - Frequency density = 4
$$30 < t\leq 50$$ - Frequency density = 0.25
Q3.Here is some data on the lengths of some parcels. Match the frequency with the class interval.
$$0 < l \leq 5$$ - 12
$$5 < l \leq 10$$ - 15
$$10 < l \leq 14$$ - 20
$$15< l \leq 16$$ - 4
Q4.Here is a histogram showing lengths of different fruit. Which numbers represent $$x$$, $$y$$ and $$z$$ on the $$y$$ axis?
Q5.Here are the times taken to type the alphabet. Match the class interval to the correct frequency.
$$0 < t \leq 10$$ - Frequency = 4
$$10 < t \leq 15$$ - Frequency = 8
$$15 < t \leq 20$$ - Frequency = 20
$$20 < t \leq 30$$ - Frequency = 16
$$30 < t\leq 50$$ - Frequency = 5
Q6.Here is a histogram showing the time it takes to solve a puzzle.
$$0 < t\leq 2$$ - Frequency = 10
$$2 < t \leq 4$$ - Frequency density = 6
$$4 < t \leq 5$$ - Frequency = 15
$$5 < t\leq 10$$ - Frequency density = 2.8
$$10 < t \leq 12$$ - Frequency density = 2.5
