To find the percentiles of a given data set, we first need to understand what percentiles are. A percentile is a measure used in statistics to indicate the value below which a given percentage of observations fall. For example, the 25th percentile is the value below which 25% of the observations may be found.
Let's proceed step-by-step to determine the 25th and 70th percentiles for the given weights of the preschool children.
The list of weights in pounds is:
[tex]\[ [30, 46, 43, 22, 26, 25, 34, 44, 50, 40, 31, 21, 49, 41, 28, 20, 37, 23, 27, 24] \][/tex]
First, order the data set in ascending order:
[tex]\[ [20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 34, 37, 40, 41, 43, 44, 46, 49, 50] \][/tex]
To find the 25th percentile, we locate the value below which 25% of the data falls. Similarly, for the 70th percentile, we locate the value below which 70% of the data falls.
However, assuming a precise computational process has been used, we should directly state the values obtained:
(a) The [tex]\(25^{\text{th}}\)[/tex] percentile is:
[tex]\[ 24.75 \text{ pounds} \][/tex]
(b) The [tex]\(70^{\text{th}}\)[/tex] percentile is:
[tex]\[ 40.3 \text{ pounds} \][/tex]
Thus, we have the following results:
(a) The [tex]\(25^{\text{th}}\)[/tex] percentile: [tex]\(24.75\)[/tex] pounds
(b) The [tex]\(70^{\text{th}}\)[/tex] percentile: [tex]\(40.3\)[/tex] pounds
