Question

the weights (in pounds) of a sample of newborn babies are listed below.
5.3 5.5 5.6 5.8 5.9 5.9 6.1 6.2 6.2 6.4
6.5 6.5 6.5 6.7 6.8 6.8 6.8 6.9 7.0 7.0
7.2 7.3 7.5 7.5 7.6 7.8 7.9 7.9 8.1 8.5
(a) find the 81st percentile.
write a sentence interpreting your answer.
(b) find the 20th percentile.
write a sentence interpreting your answer.
(c) find the percentile of a baby who weighs 6.8 pounds.
write a sentence interpreting your answer.

Explanation:

Step1: Count total data points

There are 30 data points, so $n=30$.

Step2: Calculate index for 81st percentile

Use formula $i = \frac{p}{100} \times n$, where $p=81$.
$i = \frac{81}{100} \times 30 = 24.3$

Step3: Round up to find position

Round 24.3 up to 25. The 25th value in the ordered list is 7.6.

Step4: Calculate index for 20th percentile

Use $i = \frac{20}{100} \times 30 = 6$

Step5: Average 6th and 7th values

6th value = 5.9, 7th value = 6.1. $\frac{5.9+6.1}{2}=6.0$

Step6: Count values ≤6.8 for percentile

There are 18 values ≤6.8. Use formula $\text{Percentile} = \frac{\text{Number of values } \leq x}{n} \times 100$
$\text{Percentile} = \frac{18}{30} \times 100 = 60$

Answer:

Part (a)

81st percentile: 7.6
Interpretation: 81% of the newborn babies in the sample weigh 7.6 pounds or less, and 19% weigh more than 7.6 pounds.

Part (b)

20th percentile: 6.0
Interpretation: 20% of the newborn babies in the sample weigh 6.0 pounds or less, and 80% weigh more than 6.0 pounds.

Part (c)

Percentile for 6.8 pounds: 60th
Interpretation: A newborn baby weighing 6.8 pounds weighs more than or equal to 60% of the babies in the sample, and less than 40% of the babies in the sample.