Photo AI
Fifty athletes must have access to suitable training facilities - NSC Mathematics - Question 2 - 2024 - Paper 2
Question 2
Fifty athletes must have access to suitable training facilities. The table below shows the distances, in km, that indicate how much they need to access suitable trai... show full transcript
Worked Solution & Example Answer:Fifty athletes must have access to suitable training facilities - NSC Mathematics - Question 2 - 2024 - Paper 2
Step 1
2.1 Voltooi die kumulatiefrekvensie-kolom wat in die tabel in die ANTWOORDEBOOK verskaf word.
Answer
To complete the cumulative frequency column, add the frequency of each distance segment cumulatively:
- For 0 ≤ x < 5: 7
- For 5 ≤ x < 10: 7 + 7 = 14
- For 10 ≤ x < 15: 14 + 20 = 34
- For 15 ≤ x < 20: 34 + 12 = 46
- For 20 ≤ x < 25: 46 + 3 = 49
- For 25 ≤ x < 30: 49 + 3 = 52
Thus, the cumulative frequency table would be:
| AFSTAND (x km) | KUMULATIE FREKWENSIE |
|---|---|
| 0 ≤ x < 5 | 7 |
| 5 ≤ x < 10 | 14 |
| 10 ≤ x < 15 | 34 |
| 15 ≤ x < 20 | 46 |
| 20 ≤ x < 25 | 49 |
| 25 ≤ x < 30 | 52 |
Step 2
2.2 Op die rooster wat in die ANTWOORDEBOOK verskaf word, teken 'n kumulatiefreekwensie-kromme (ogief) om die data hierbo te verteenwoordig.
Answer
To plot the cumulative frequency ogive:
- Use the upper limits of the distance intervals for the x-axis (e.g., 5, 10, 15, 20, 25, 30).
- Plot the cumulative frequencies on the y-axis based on the previously calculated values.
- Connect the points with a smooth line to form the ogive.
Step 3
Step 4
2.4 Die gesigneerde van 4 van die atlete hierso het tussen 15 en 20 km vanaf in geskikte oefenfasiliteit woon, besluit om 10 kilometer ander te daat die fasiliteit te rek. in water interval sal hierdie atlete toeneem?
Answer
If 4 athletes who lived within 15 and 20 km consider moving 10 km away, they will now fall into a new distance interval. The new distribution needs to be analyzed based on the original frequency table. Since athletes are moving away, the frequency in the 15 ≤ x < 20 category will decrease and new categories would need to be created based on their new distances.
Step 5
2.5 Die geskatte gemiddelde afstand van die atlete hanteer met nadat die atlete 10 kilometer ander tot die afsnit van 5, 7, 12, 20, 17, 5, 22, 5 en 27, 5.
Answer
To estimate the mean distance of the athletes:
- Calculate the sum of distances for the revised counts: ext{Estimated mean} = rac{(2.5 imes 7) + (7.5 imes 7) + (12.5 imes 20) + (17.5 imes 12) + (22.5 imes 3) + (27.5 imes 3)}{50} = rac{675}{50} = 13.5 ext{ km}
Thus, the estimated mean is 13.5 km.