Find the 16th percentile (P16) of the following weights of 30 newborn babies: 5.5, 5.7, 5.8, 5.9, 6.1, 6.1, 6.4, 6.4, 6.5, 6.6, 6.7, 6.7, 6.7, 6.9, 7.0, 7.0, 7.0, 7.1, 7.2, 7.2, 7.... Find the 16th percentile (P16) of the following weights of 30 newborn babies: 5.5, 5.7, 5.8, 5.9, 6.1, 6.1, 6.4, 6.4, 6.5, 6.6, 6.7, 6.7, 6.7, 6.9, 7.0, 7.0, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.7, 7.7, 7.8, 8.0, 8.1, 8.1, 8.3, 8.7. Read more

Steps to Solve

1. Organize the data
   First, sort the weights of the 30 newborn babies in ascending order. This step is crucial as percentiles are determined based on ordered data.

2. Calculate the index for P16
   Use the formula to find the index of the 16th percentile. The formula is:
   $$ P_k = \frac{k}{100} \times (N + 1) $$
   Where (k) is the percentile (16 in this case) and (N) is the number of data points (30). So we calculate:
   $$ P_{16} = \frac{16}{100} \times (30 + 1) = 0.16 \times 31 = 4.96 $$

3. Interpret the index
   Since 4.96 is not a whole number, we round it up to 5. This means the 16th percentile is the value of the 5th baby in the sorted list.

4. Identify the 5th value
   From the sorted list of weights, find the weight corresponding to the 5th index. This will be the 16th percentile of the weights.