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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 - Edexcel - A-Level Maths Statistics - Question 5 - 2007 - Paper 1
Question 5
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.
Answer
A histogram is suitable for this data because it represents continuous data effectively, allowing for the visualization of the frequency distribution of time spent watching television. This conveys information about the distribution shape and enables easier understanding of the data across intervals.
Step 2
Step 3
Show that on this histogram each child was represented by 0.8 cm².
Answer
To determine the area corresponding to each child, we first calculate the total area of the rectangle representing the class 20–29:
Area = height × width = 3.6 ext{ cm} imes 2 ext{ cm} = 7.2 ext{ cm}².
Given the frequency of this class is 9, the area corresponding to each child can be calculated as follows:
Each child area = rac{7.2 ext{ cm}²}{9} = 0.8 ext{ cm}².
Step 4
Find the total number of children in the group.
Answer
The total area under the histogram is given as 24 cm². Since each child represents an area of 0.8 cm², the total number of children in the group can be found using:
Total number of children = rac{24 ext{ cm}²}{0.8 ext{ cm}²} = 30.
Therefore, the total number of children in the group is 30.