Find the 5 number summary for the data shown



12

18

19

32

42

48

50

64

67

76

80

82

85

96

98


5 number summary:

The five-number summary consists of the following key values from a data set: **minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum**. Let's find these values for the given data set:

### Data:
12, 18, 19, 32, 42, 48, 50, 64, 67, 76, 80, 82, 85, 96, 98

#### 1. **Minimum**: The smallest number in the data set.
\[
\text{Minimum} = 12
\]

#### 2. **Maximum**: The largest number in the data set.
\[
\text{Maximum} = 98
\]

#### 3. **Median (Q2)**: The middle value in the ordered data set.
There are 15 numbers, so the median is the 8th value.
\[
\text{Median} = 64
\]

#### 4. **First Quartile (Q1)**: The median of the lower half of the data set (excluding the median).
The lower half of the data is: 12, 18, 19, 32, 42, 48, 50
The median of these values (7 numbers) is the 4th value.
\[
\text{Q1} = 32
\]

#### 5. **Third Quartile (Q3)**: The median of the upper half of the data set (excluding the median).
The upper half of the data is: 67, 76, 80, 82, 85, 96, 98
The median of these values (7 numbers) is the 4th value.
\[
\text{Q3} = 82
\]

### **Five-number summary**:
\[
\boxed{12, 32, 64, 82, 98}
\]

Would you like more details or further explanation on any of these steps?

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Here are some related questions to expand on this topic:

1. How is the interquartile range (IQR) calculated from the five-number summary?
2. What is the difference between a five-number summary and a box plot?
3. How would outliers be identified using the five-number summary?
4. Can the five-number summary be used for non-numerical data sets?
5. What are the advantages of using the five-number summary in data analysis?

**Tip**: The interquartile range (IQR) is often used to detect outliers, as any data point below \(Q1 - 1.5 \times IQR\) or above \(Q3 + 1.5 \times IQR\) is typically considered an outlier.

Find the 5 number summary for the data shown: 12, 18, 19, 32, 42, 48, 50, 64, 67, 76, 80, 82, 85, 96, 98

Learn how to calculate the five-number summary for the data set: 12, 18, 19, 32, 42, 48, 50, 64, 67, 76, 80, 82, 85, 96, 98. This tutorial explains how to find the minimum, maximum, median (Q2), first quartile (Q1), and third quartile (Q3). Suitable for students in Grades 6-8.

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