Here is a set of sample data.


32

6

26

60

80

36

29

100

74

21

99

67

24

43

66

58

89

90

38

10

59

75

69

86

Base on the data above, identify the 5 number summary 

To identify the 5-number summary for the given data set, we'll follow these steps:

### Step 1: List all the values in ascending order

The given data is:

\[32, 6, 26, 60, 80, 36, 29, 100, 74, 21, 99, 67, 24, 43, 66, 58, 89, 90, 38, 10, 59, 75, 69, 86\]

Arranging these values in ascending order:

\[6, 10, 21, 24, 26, 29, 32, 36, 38, 43, 58, 59, 60, 66, 67, 69, 74, 75, 80, 86, 89, 90, 99, 100\]

### Step 2: Calculate the 5-number summary

1. **Minimum:** The smallest value in the data set.
   - \( \text{Min} = 6 \)

2. **Maximum:** The largest value in the data set.
   - \( \text{Max} = 100 \)

3. **Median (Q2):** The middle value of the data set.
   - Since there are 24 values, the median will be the average of the 12th and 13th values:
   - Median \( Q2 = \frac{59 + 60}{2} = 59.5 \)

4. **First Quartile (Q1):** The median of the lower half of the data.
   - The lower half includes the first 12 values: \[6, 10, 21, 24, 26, 29, 32, 36, 38, 43, 58, 59\]
   - \( Q1 = \frac{29 + 32}{2} = 30.5 \)

5. **Third Quartile (Q3):** The median of the upper half of the data.
   - The upper half includes the last 12 values: \[60, 66, 67, 69, 74, 75, 80, 86, 89, 90, 99, 100\]
   - \( Q3 = \frac{75 + 80}{2} = 77.5 \)

### Final 5-number summary:
- **Minimum:** 6
- **First Quartile (Q1):** 30.5
- **Median (Q2):** 59.5
- **Third Quartile (Q3):** 77.5
- **Maximum:** 100

Would you like more details or have any other questions?

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Here are 5 related questions for further exploration:
1. How does the mean compare to the median in this data set?
2. What does the interquartile range (IQR) tell you about the spread of the middle 50% of data?
3. How would the 5-number summary change if an outlier was added to this data set?
4. Can you identify any potential outliers in this data set?
5. How does the 5-number summary help in constructing a box plot?

**Tip:** Always ensure that data is sorted correctly before calculating the quartiles for an accurate 5-number summary.

Learn how to identify the 5-number summary of a dataset with a step-by-step explanation. This problem covers descriptive statistics concepts including quartiles and the median. Suitable for students in Grades 9-12.

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