Questions: Using the following stem leaf plot, find the five number summary, range and interquartile range for the data. 1 0 2 2 1 2 4 9 9 Key: 1 0=10

Transcript text: Using the following stem & leaf plot, find the five number summary, range and interquartile range for the data. \begin{tabular}{l|llllll} 1 & 0 & 2 & & & & \\ 2 & 1 & 2 & 4 & 9 & 9 \end{tabular} Key: $1 \mid 0=10$

Solution

Solution Steps

Step 1: Extracting Data

From the given stem-and-leaf plot, the data points are extracted as follows: \[ \text{Data} = [10, 12, 21, 22, 24, 29, 29] \]

Step 2: Calculating the Five-Number Summary

The five-number summary consists of the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum values.

Minimum: \[ \text{Min} = 10 \]
First Quartile ($Q_1$): Using the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.25 \times (7 + 1) = 2.0 \] The quantile is at position 2, which corresponds to the value: \[ Q_1 = 12 \]
Median ($Q_2$): Using the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.5 \times (7 + 1) = 4.0 \] The quantile is at position 4, which corresponds to the value: \[ Q_2 = 22 \]
Third Quartile ($Q_3$): Using the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.75 \times (7 + 1) = 6.0 \] The quantile is at position 6, which corresponds to the value: \[ Q_3 = 29 \]
Maximum: \[ \text{Max} = 29 \]

Step 3: Calculating the Range

The range is calculated as: \[ \text{Range} = \text{Max} - \text{Min} = 29 - 10 = 19 \]

Step 4: Calculating the Interquartile Range (IQR)

The interquartile range is calculated as: \[ \text{IQR} = Q_3 - Q_1 = 29 - 12 = 17 \]

Final Answer

The five-number summary, range, and interquartile range are as follows:

Min: $10$
$Q_1: 12$
Median: $22$
$Q_3: 29$
Max: $29$
Range: $19$
Interquartile Range: $17$

Thus, the final boxed answers are: \[ \boxed{\text{Min} = 10, \, Q_1 = 12, \, \text{Median} = 22, \, Q_3 = 29, \, \text{Max} = 29, \, \text{Range} = 19, \, \text{IQR} = 17} \]

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