Compute the $$ 50^{ ext {th }} $$ percentile for the following data. $$ 10,15,17,21,25,12,16,11,13,22 $$ $$ \begin{array}{l} ext { O } 13.3 \ \frac{18.5}{} \ 17.7\end{array} $$

Question

Compute the $$ 50^{	ext {th }} $$ percentile for the following data. $$ 10,15,17,21,25,12,16,11,13,22 $$ $$ \begin{array}{l}	ext { O } 13.3 \ \frac{18.5}{} \ 17.7\end{array} $$

UpStudy AI · Accepted Answer

To compute the $$ 50^{\text{th}} $$ percentile (also known as the median) for the given data set, we will follow these steps:

1. **Organize the data in ascending order.**
2. **Determine the position of the median.**
3. **Calculate the median based on the position.**

### Step 1: Organize the Data

The given data set is:
$$ 10, 15, 17, 21, 25, 12, 16, 11, 13, 22 $$

First, we will sort this data in ascending order:
$$ 10, 11, 12, 13, 15, 16, 17, 21, 22, 25 $$

### Step 2: Determine the Position of the Median

The median is the middle value of a data set. If the number of observations $$ n $$ is odd, the median is the value at position $$ \frac{n+1}{2} $$. If $$ n $$ is even, the median is the average of the values at positions $$ \frac{n}{2} $$ and $$ \frac{n}{2} + 1 $$.

In this case, we have $$ n = 10 $$ (which is even). Therefore, we will find the median using the following positions:
- $$ \frac{n}{2} = \frac{10}{2} = 5 $$
- $$ \frac{n}{2} + 1 = 5 + 1 = 6 $$

### Step 3: Calculate the Median

Now we will find the values at positions 5 and 6 in the sorted data:
- Position 5: $$ 15 $$
- Position 6: $$ 16 $$

Now, we calculate the median:
$$
\text{Median} = \frac{15 + 16}{2} = \frac{31}{2} = 15.5
$$

Thus, the $$ 50^{\text{th}} $$ percentile (median) for the given data is $$ 15.5 $$.
The $$ 50^{\text{th}} $$ percentile (median) of the data is $$ 15.5 $$.

Compute the \( 50^{\text {th }} \) percentile for the following data. \( 10,15,17,21,25,12,16,11,13,22 \) \( \begin{array}{l}\text { O } 13.3 \\ \frac{18.5}{} \\ 17.7\end{array} \)

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