Question

The weights (in pounds) of 15 preschool children are42, 46, 31, 45, 49, 37, 47, 25, 50, 30, 48, 43, 35, 39, 29Send data to calculatorFind 10th and 75th percentiles for these weights.(If necessary, consult a list of formulas.)(a)(b)The 10th percentile: 9 poundsThe 75th percentile: pounds

Answer 1

ANSWER:

The 10th percentile: 27.4 pounds

The 75th percentile: 47 pounds

EXPLANATION:

Given:

42, 46, 31, 45, 49, 37, 47, 25, 50, 30, 48, 43, 35, 39, 29

To find:

The 10th and 75th percentiles

Step-by-step solution:

Step 1: Arrange the data in ascending order

25, 29, 30, 31, 35, 37, 39, 42, 43, 45, 46, 47, 48, 49, 50

Step 2: Use the percentile rank formula to determine the 10th percentile;

$Percentile\text{ }rank=\frac{p}{100}(n+1)$

where;

p = the percentile

n = total number of items in the data set

where p = 10 and n = 15, we'll have;

$\begin{gathered} Percentile\text{ }rank=\frac{10}{100}(15+1) \\ \\ =\frac{1}{10}(16) \\ \\ =1.6 \end{gathered}$

Since the rank is not an integer, we'll go ahead and use the interpolation method as seen below;

$\begin{gathered} 1.6-1=0.6 \\ \\ 10th\text{ percentile}=25+0.6(29-25) \\ \\ =25+0.6(4) \\ \\ =25+2.4 \\ \\ =27.4 \end{gathered}$

Therefore, the 10th percentile is 27.4 pounds

Where p = 75 and n = 15, we'll have;

$\begin{gathered} Percentile\text{ }rank=\frac{75}{100}(15+1) \\ \\ =\frac{75}{100}(16) \\ \\ =12 \end{gathered}$

Since the rank is an integer, we can see that the 75th percentile is 47 pounds