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Two companies carried out different surveys - Junior Cycle Mathematics - Question 3 - 2016
Question 3
Two companies carried out different surveys. The results of Company A's survey are shown in the table below. Company A Question: Does your hair feel nicer when you... show full transcript
Worked Solution & Example Answer:Two companies carried out different surveys - Junior Cycle Mathematics - Question 3 - 2016
Step 1
Use the numbers in the table to draw a pie chart for Company A's results in the space above.
Answer
To calculate the angles for the pie chart, we need to find the proportions of responses:
- Total Respondents = 300
- Number Yes = 280
- Number No = 20
Calculating the angle for 'Yes':
Angle for Yes = ( \frac{280}{300} \times 360 = 336^\circ )
Calculating the angle for 'No':
Angle for No = ( \frac{20}{300} \times 360 = 24^\circ )
Thus, the pie chart will have:
- 336° for Yes
- 24° for No
Label these clearly on the pie chart.
Step 2
In this survey, people had to answer Yes or No. Put a tick in the correct box to show what type of data this is. Give a reason for your answer.
Answer
Type of data:
- Categorical ✔️
- Numerical
Reason: The data is categorical because the responses are categorically divided into two options: Yes and No, which are not numerical.
Step 3
Work out how many people answered No and how many people answered Yes in Company B's survey.
Answer
Total surveyed by Company B = 72
- Size of No angle = 50°
- Size of Yes angle = 310°
Using the angles to find the number of respondents:
( Number No = \frac{50}{360} \times 72 = 10 )
( Number Yes = 72 - 10 = 62 )
Thus, Number No = 10 and Number Yes = 62.
Step 4
Based on the total numbers of people surveyed, which company's results do you think are more reliable? Give a reason for your answer.
Answer
Company whose results are more reliable: Company A ✔️
Reason: Company A surveyed a larger number of respondents (300) compared to Company B (72), making its results more statistically reliable.