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16 girls and 14 boys went on a school tour to Barcelona - Junior Cycle Mathematics - Question 6 - 2018
Question 6
16 girls and 14 boys went on a school tour to Barcelona. The weight of each student’s bag (in kg) is shown in the tables below. Girls 5.8 6 6.9 7.6 7.8 8 8.... show full transcript
Worked Solution & Example Answer:16 girls and 14 boys went on a school tour to Barcelona - Junior Cycle Mathematics - Question 6 - 2018
Step 1
Mean weight of the boys' bags
Answer
To calculate the mean weight of the boys’ bags, we first sum the weights of all the boys’ bags. From the table, the weights are: 5.9, 6.8, 7.4, 8.5, 6.8, 8.7, 8.4, 8.9, 9.4, 9.5, 9.7, 10.5.
Total weight = 5.9 + 6.8 + 7.4 + 8.5 + 6.8 + 8.7 + 8.4 + 8.9 + 9.4 + 9.5 + 9.7 + 10.5 = 104.9 kg
Number of boys = 14.
Mean weight = Total weight / Number of boys = 104.9 / 14 = 7.49 kg.
Therefore, the mean weight of the boys’ bags, correct to one decimal place, is 7.5 kg.
Step 2
Complete the frequency table
Answer
Based on the weight data:
-
For Girls:
- 5 – 6 kg: 2 bags
- 6 – 7 kg: 1 bag
- 7 – 8 kg: 3 bags
- 8 – 9 kg: 7 bags
- 9 – 10 kg: 1 bag
- 10 – 11 kg: 0 bags
- 11 – 12 kg: 0 bags
-
For Boys:
- 5 – 6 kg: 1 bag
- 6 – 7 kg: 4 bags
- 7 – 8 kg: 6 bags
- 8 – 9 kg: 1 bag
- 9 – 10 kg: 0 bags
- 10 – 11 kg: 0 bags
- 11 – 12 kg: 0 bags
Fill the frequencies in the table accordingly.
Step 3
Is Eoin correct?
Answer
No, Eoin is not correct.
Reason:
- The mean weight of the girls' bags (8.6 kg) is greater than the mean weight of the boys' bags (7.5 kg).
- This indicates that the girls took heavier bags than the boys did. However, examining the distribution gives similar values indicating the variations are not statistically significant.
Step 4
Draw a histogram
Answer
The histogram should reflect the number of students against the time taken to get through security.
- On the x-axis, represent the time intervals (0-5, 5-10, 10-15, 15-20, 20-25, 25-30 minutes).
- On the y-axis, represent the number of students.
- Plot bars corresponding to the number of students in each time interval:
- 0-5: 4
- 5-10: 8
- 10-15: 11
- 15-20: 6
- 20-25: 0
- 25-30: 1
Ensure each bar is labelled clearly.
Step 5
Estimate mean amount of money spent
Answer
To estimate the mean amount spent, we use mid-interval values:
- For £0-5: mid-value = 2.5, frequency = 5
- For £5-10: mid-value = 7.5, frequency = 4
- For £10-20: mid-value = 15, frequency = 7
- For £20-30: mid-value = 25, frequency = 8
- For £30-50: mid-value = 40, frequency = 3
- For £50-100: mid-value = 75, frequency = 1
- For £100-150: mid-value = 125, frequency = 2
Now calculate:
Total amount = (2.55 + 7.54 + 157 + 258 + 403 + 751 + 125*2) = 792.5
Total students = 30.
Mean = Total amount / Total students = 792.5 / 30 = 26.416...
So the estimated mean amount of money spent is £26.42.
Step 6
Estimate median amount of money spent
Answer
To find the median:
- The total number of students is 30, thus the median will be the average of the 15th and 16th values.
- Counting through the cumulative frequencies based on the frequency table:
- Up to 0-5: 5
- Up to 5-10: 5+4 = 9
- Up to 10-20: 9+7 = 16
Thus, both the 15th and 16th students fall within the 10-20 category, where the values are 10 to 20.
Therefore, the median can be estimated to be between £15 and £20, specifically closer to £18.