In a survey, 1500 people were asked which national radio station they normally listen to - Junior Cycle Mathematics - Question 7 - 2012
Question 7
In a survey, 1500 people were asked which national radio station they normally listen to.
The results of the survey are given in the table below.
| Frequency |... show full transcript
Worked Solution & Example Answer:In a survey, 1500 people were asked which national radio station they normally listen to - Junior Cycle Mathematics - Question 7 - 2012
Step 1
How many of the people surveyed do not listen to a national radio station?
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Answer
To find the number of people who do not listen to a national radio station, we first sum the frequencies of those who listen to a national station:
375+195+120+45+165=900
Then, subtract this sum from the total number of people surveyed:
1500−900=600
Thus, 600 people do not listen to a national radio station.
Step 2
Complete the table above.
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Answer
| Relative frequency (as a fraction) | 375/1500 | 195/1500 | 120/1500 | 45/1500 | 165/1500 | 600/1500 |
| Relative frequency (as a decimal) | 0.25 | 0.13 | 0.08 | 0.03 | 0.11 | 0.40 |
Step 3
Find the sum of the relative frequencies written as fractions.
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Answer
The sum of the relative frequencies written as fractions is:
Find the sum of the relative frequencies written as decimals.
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Answer
The sum of the relative frequencies written as decimals is:
0.25+0.13+0.08+0.03+0.11+0.40=1.00
Step 5
Jackie wrote the relative frequencies as percentages. She found their sum to be 80%. Do you think her calculations are correct? Give a reason for your answer.
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Answer: No.
Reason: They should add up to 100% (or 1.0 in decimal), not 80%.
Step 6
Denis looked at the data and said "I can find out how many people in the survey normally listen to local radio." Do you agree or disagree with Denis? Explain your answer.
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Answer
Answer: No.
Explanation: Some people may not listen to any radio at all.
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