The most accurate, evidence based range of normal pediatric vital signs that I know of are from Fleming 2011:
Heart rate
Respiratory rate
PALS normal vital signs
The more common vital signs you will encounter are from the PALS guidelines:
| Age | Heart rate | Resp rate | Systolic BP |
| Newborn | 90-180 | 40-60 | 60-90 |
| 1 month | 110-180 | 30-50 | 70-104 |
| 3 months | 110-180 | 30-45 | 70-104 |
| 6 months | 110-180 | 25-35 | 72-110 |
| 1 year | 80-160 | 20-30 | 72-110 |
| 2 years | 80-140 | 20-28 | 74-110 |
| 4 years | 80-120 | 20-26 | 78-112 |
| 6 years | 75-115 | 18-24 | 82-115 |
| 8 years | 70-110 | 18-22 | 86-118 |
| 10 years | 70-110 | 16-20 | 90-121 |
| 12 years | 60-110 | 16-20 | 90-126 |
| 14 years | 60-100 | 16-20 | 92-130 |
References
Fleming S et al. Normal Ranges of Heart Rate and Respiratory Rate in Children from Birth to 18 Years of Age: A Systematic Review of Observational Studies. Lancet 2011; 377: 1011-18. PDF