Questions: The weights (in pounds) of 19 preschool children are 24,47,48,44,28,43,22,35,29,34,23,26,31,36,21,41,40,32,46 Find 25th and 70th percentiles for these weights. (a) The 25th percentile: II pounds (b) The 70th percentile: pounds

The weights (in pounds) of 19 preschool children are
24,47,48,44,28,43,22,35,29,34,23,26,31,36,21,41,40,32,46
Find 25th and 70th percentiles for these weights.
(a) The 25th percentile: II pounds
(b) The 70th percentile: pounds

Transcript text: The weights (in pounds) of 19 preschool children are \[ 24,47,48,44,28,43,22,35,29,34,23,26,31,36,21,41,40,32,46 \] Find $25^{\text {th }}$ and $70^{\text {th }}$ percentiles for these weights. (a) The $25^{\text {th }}$ percentile: II pounds (b) The $70^{\text {th }}$ percentile: $\square$ pounds

Solution

Solution Steps

Step 1: Sort the Data

The sorted dataset is: [21, 22, 23, 24, 26, 28, 29, 31, 32, 34, 35, 36, 40, 41, 43, 44, 46, 47, 48].

Step 2: Calculate the Position

Using the formula $i = \frac{P}{100} \times (N + 1)$, we find the position $i = 5$.

Step 3: Determine the Percentile Value

Since $i$ is an integer, the value at position $i$ in the sorted list is the $P^{\text{th}}$ percentile.

Final Answer: The 25th percentile of the dataset is 26.

Step 1: Sort the Data

The sorted dataset is: [21, 22, 23, 24, 26, 28, 29, 31, 32, 34, 35, 36, 40, 41, 43, 44, 46, 47, 48].

Step 2: Calculate the Position

Using the formula $i = \frac{P}{100} \times (N + 1)$, we find the position $i = 14$.

Step 3: Determine the Percentile Value

Since $i$ is an integer, the value at position $i$ in the sorted list is the $P^{\text{th}}$ percentile.

Final Answer: The 70th percentile of the dataset is 41.

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