A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample. The times were summarised in a grouped frequency table and represented by a histogram. One of the classes in the grouped frequency distribution was 20–29 and its associated frequency was 9. On the histogram the height of the rectangle representing that class was 3.6 cm and the width was 2 cm. (a) Give a reason to support the use of a histogram to represent these data. (b) Write down the underlying feature associated with each of the bars in a histogram. (c) Show that on this histogram each child was represented by 0.8 cm². The total area under the histogram was 24 cm². (d) Find the total number of children in the group.

A-Level Edexcel Maths Statistics Working with Data: A teacher recorded, to the neare

A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample - Edexcel - A-Level Maths Statistics - Question 5 - 2007 - Paper 1

Question 5

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A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample. The times were summarised in a... show full transcript

Worked Solution & Example Answer:A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample - Edexcel - A-Level Maths Statistics - Question 5 - 2007 - Paper 1

Step 1

Give a reason to support the use of a histogram to represent these data.

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Answer

A histogram is appropriate for representing continuous data like time spent watching television, as it allows for the visualization of the distribution of the data across various intervals (bins). This format effectively communicates both the frequency and the shape of the distribution.

Step 2

Write down the underlying feature associated with each of the bars in a histogram.

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Answer

The underlying feature associated with each bar in a histogram is the frequency density, which represents the number of observations per unit of the continuous variable that each bar spans.

Step 3

Show that on this histogram each child was represented by 0.8 cm².

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Answer

To find the area of the rectangular bar representing the class 20-29:

Area = height × width = 3.6 ext{ cm} imes 2 ext{ cm} = 7.2 ext{ cm}².

Since the class frequency is 9, we need to calculate the area per child:

ext{Area per child} = rac{7.2 	ext{ cm}²}{9} = 0.8 	ext{ cm}².

Step 4

Find the total number of children in the group.

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Answer

Given that the total area under the histogram is 24 cm² and each child is represented by 0.8 cm², we can find the total number of children by using the formula:

ext{Number of children} = rac{	ext{Total area}}{	ext{Area per child}} = rac{24 	ext{ cm}²}{0.8 	ext{ cm}²} = 30.

Therefore, the total number of children in the group is 30.

A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample - Edexcel - A-Level Maths Statistics - Question 5 - 2007 - Paper 1

Worked Solution & Example Answer:A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample - Edexcel - A-Level Maths Statistics - Question 5 - 2007 - Paper 1

Give a reason to support the use of a histogram to represent these data.

Write down the underlying feature associated with each of the bars in a histogram.

Show that on this histogram each child was represented by 0.8 cm².

Find the total number of children in the group.

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