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To find the five-number summary, we'll first need to gather the data points and then calculate the following statistics:

1. **Minimum** - The smallest number in the dataset.
2. **First Quartile (Q1)** - The median of the lower half of the dataset.
3. **Median (Q2)** - The middle number of the entire dataset.
4. **Third Quartile (Q3)** - The median of the upper half of the dataset.
5. **Maximum** - The largest number in the dataset.

### Step 1: Arrange the Data in Order
The data points are:
\[
37, 56, 42, 27, 68, 60, 96, 57, 51, 12
\]

Arranging them in ascending order:
\[
12, 27, 37, 42, 51, 56, 57, 60, 68, 96
\]

### Step 2: Calculate the Five-Number Summary
1. **Minimum**: The smallest number is \(12\).
2. **Median (Q2)**: Since there are 10 data points, the median is the average of the 5th and 6th numbers:  
   \[
   \text{Median} = \frac{51 + 56}{2} = 53.5
   \]
3. **First Quartile (Q1)**: This is the median of the lower half, which is the first 5 numbers: \(12, 27, 37, 42, 51\).  
   The median of these is the 3rd number:
   \[
   Q1 = 37
   \]
4. **Third Quartile (Q3)**: This is the median of the upper half, which is the last 5 numbers: \(56, 57, 60, 68, 96\).  
   The median of these is the 3rd number:
   \[
   Q3 = 60
   \]
5. **Maximum**: The largest number is \(96\).

### Five-Number Summary
The five-number summary is:
\[
12, 37, 53.5, 60, 96
\]

Would you like further details or have any questions?

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Here are 5 related questions to deepen your understanding:
1. How would the five-number summary change if an additional data point was added to the dataset?
2. Why is the median (Q2) calculated by averaging the middle two numbers for even-numbered datasets?
3. How does the five-number summary help in understanding the spread of a dataset?
4. What is the Interquartile Range (IQR) and how is it calculated using the five-number summary?
5. How does identifying outliers relate to the five-number summary?

**Tip:** When arranging data to find quartiles, make sure to count carefully, especially with an even number of data points, as it affects the calculation of the median.

Find the 5 number summary for the data set {37, 42, 68, 96, 51, 56, 27, 60, 57, 12}.

Find the five-number summary for the data set {37, 42, 68, 96, 51, 56, 27, 60, 57, 12}. Learn how to calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum with this detailed solution.

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