Sixth grade $$ \quad 31.7 $$ Calculate quartiles and interquartile range MNV In the data set below, what is the upper quartile? $$ \begin{array}{lllllll}59 & 59 & 60 & 66 & 68 & 68 & 72\end{array} 73 $$

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UpStudy AI · Accepted Answer

To find the **upper quartile (Q₃)** of the given data set, let's follow these steps:

### **1. Organize the Data in Ascending Order**
The data set you provided is already in ascending order:

$$59, \, 59, \, 60, \, 66, \, 68, \, 68, \, 72, \, 73$$

### **2. Determine the Median (Second Quartile, Q₂)**
The median divides the data set into two equal halves.

- **Number of data points (N):** 8
- Since $$N$$ is even, the median is the average of the 4th and 5th numbers.

$$
\text{Median (Q₂)} = \frac{66 + 68}{2} = \frac{134}{2} = 67
$$

### **3. Find the Lower Quartile (First Quartile, Q₁)**
The lower quartile is the median of the lower half of the data.

- **Lower half:** $$59, \, 59, \, 60, \, 66$$
- Number of data points in lower half: 4

$$
\text{Lower Quartile (Q₁)} = \frac{59 + 60}{2} = \frac{119}{2} = 59.5
$$

### **4. Find the Upper Quartile (Third Quartile, Q₃)**
The upper quartile is the median of the upper half of the data.

- **Upper half:** $$68, \, 68, \, 72, \, 73$$
- Number of data points in upper half: 4

$$
\text{Upper Quartile (Q₃)} = \frac{68 + 72}{2} = \frac{140}{2} = 70
$$

### **5. Calculate the Interquartile Range (IQR)**
The interquartile range measures the spread of the middle 50% of the data.

$$
\text{IQR} = Q₃ - Q₁ = 70 - 59.5 = 10.5
$$

### **Summary**
- **Lower Quartile (Q₁):** 59.5
- **Median (Q₂):** 67
- **Upper Quartile (Q₃):** **70**
- **Interquartile Range (IQR):** 10.5

**Answer:** The upper quartile of the data set is **70**.
The upper quartile is 70.

Sixth grade Calculate quartiles and interquartile range MNV
In the data set below, what is the upper quartile?

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Solución

1. Organize the Data in Ascending Order

2. Determine the Median (Second Quartile, Q₂)

3. Find the Lower Quartile (First Quartile, Q₁)

4. Find the Upper Quartile (Third Quartile, Q₃)

5. Calculate the Interquartile Range (IQR)

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Sixth grade Calculate quartiles and interquartile range MNV In the data set below, what is the upper quartile?