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Clara asked all of the students in her school some questions about their eating and exercise - Junior Cycle Mathematics - Question 6 - 2017
Question 6
Clara asked all of the students in her school some questions about their eating and exercise. One of Clara’s questions was: How healthy is your diet? Tick one box.... show full transcript
Worked Solution & Example Answer:Clara asked all of the students in her school some questions about their eating and exercise - Junior Cycle Mathematics - Question 6 - 2017
Step 1
Find the probability that a student chosen at random from those surveyed ticked “Very healthy” or “Fairly healthy”
Answer
To find the probability, we first need to determine the total number of students surveyed, which is the sum of those in each category. From the given data, the number of students who ticked 'Very healthy' is 150 and those who ticked 'Fairly healthy' is 170.
Total number of students surveyed:
egin{align*}
ext{Total} &= 150 + 170 + ext{(Number of Not Very Healthy)} + ext{(Number of Very Unhealthy)}
&= 150 + 170 + 120 + 72 \ ext{(from calculations in part (b))}
&= 512
ext{Probability} (P)\ ext{P(ticked ‘Very healthy’ or ‘Fairly healthy’)} &= rac{150 + 170}{512} = rac{320}{512} = rac{5}{8}
\ ext{So, } P = 0.625.
Step 2
Complete the table above.
Answer
Calculating the remaining entries:
For 'Not very healthy', we can derive:
egin{align*} (90° ext{ represents } 150 ext{ students}) ightarrow (360° = 4 imes 150)\ ext{Let x be the number of students in 'Not very healthy', hence:}\12 \text{ Stripe + (Additional Angle)}\ ext{Thus, } (x ext{ students}) = (360° ÷ 150) = 120°\ => ext{Number of Not Very Healthy} = 120.\ \ ext{For 'Very unhealthy', we have:}\ \text{Total = 360°}\ ext{Total Angles = 96° + 90° + x + y = 360°}\ ext{Fast forward and solving we get:}\ x = 72 \ => ext{Number of Very Unhealthy} = 72.
Now, the completed table will look as follows:
| Category | Number of students | Size of Angle (degrees) |
|---|---|---|
| Very healthy | 150 | 96° |
| Fairly healthy | 170 | 90° |
| Not very healthy | 120 | 102° |
| Very unhealthy | 72 | 72° |
Step 3
Complete the table below to show one question in each case that Clara could ask that would generate each type of data.
Answer
For the types of data, Clara could frame questions as follows:
- Numerical continuous: How much water do you drink each day? (This generates continuous numerical data.)
- Numerical discrete: How many press-ups can you do in 30 seconds? (This is a discrete count.)
- Categorical ordinal: How healthy is your diet? Tick one box. (This is already given.)
- Categorical nominal: Which do you prefer, pizza or salad? (This provides nominal data, categorizing preference without ranking.)
Step 4
Explain why it is important to have a representative sample when doing statistical research.
Answer
Having a representative sample is essential in statistical research to ensure the results reflect the population accurately. A representative sample helps to eliminate biases, providing a more accurate view of the broader population's opinions or behaviors. This leads to better generalizations and predictions based on the collected data, enhancing the reliability and validity of the research findings.