Questions: Using the given data, find the following. 28 23 9 3 16 Part: 0 / 2 Part 1 of 2 Identify the five-number summary. Round your answers to one decimal place as needed. Low = Q1= , MD = , Q3= , High =

Using the given data, find the following.
28 23 9 3 16
Part: 0 / 2

Part 1 of 2

Identify the five-number summary. Round your answers to one decimal place as needed.
Low =
Q1= , MD = , Q3= , High =

Transcript text: Using the given data, find the following. \[ \begin{array}{lllll} 28 & 23 & 9 & 3 & 16 \end{array} \] Part: $0 / 2$ Part 1 of 2 Identify the five-number summary. Round your answers to one decimal place as needed. Low $=$ $\square$ $\square$ $Q_{1}=$ , MD = $\square$ , $Q_{3}=$ $\square$ , High = $\square$

Solution

Solution Steps

Step 1: Sort the Data

The given data is $ [28, 23, 9, 3, 16] $. After sorting, we obtain: \[ \text{Sorted data} = [3, 9, 16, 23, 28] \]

Step 2: Calculate the Five-Number Summary

The five-number summary consists of the following components:

Low: The minimum value in the sorted data, which is: \[ \text{Low} = 3 \]
High: The maximum value in the sorted data, which is: \[ \text{High} = 28 \]

Step 3: Calculate $ Q_1 $ (First Quartile)

To find $ Q_1 $, we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.25 \times (5 + 1) = 1.5 \] Since the rank is $ 1.5 $, we average the values at positions 1 and 2: \[ Q_1 = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{3 + 9}{2} = 6.0 \]

Step 4: Calculate the Median ($ Q_2 $)

To find the median, we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.5 \times (5 + 1) = 3.0 \] The median corresponds to the value at position 3: \[ \text{Median} = 16 \]

Step 5: Calculate $ Q_3 $ (Third Quartile)

To find $ Q_3 $, we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.75 \times (5 + 1) = 4.5 \] Since the rank is $ 4.5 $, we average the values at positions 4 and 5: \[ Q_3 = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{23 + 28}{2} = 25.5 \]