Use the accompanying data set to complete the following actions.
a. Find the quartiles.
b. Find the interquartile range.
c. Identify any outliers.
585662555456596463655855586381 ,
a. Find the quartiles.
The first quartile, , is 56 .
The second quartile, , is 62 .
The third quartile, , is 63 .
(Type integers or decimals.)

Ask by Rodriquez O'Quinn. in the United States

Jan 10,2025

Question

Use the accompanying data set to complete the following actions.
a. Find the quartiles.
b. Find the interquartile range.
c. Identify any outliers.
585662555456596463655855586381 ,
a. Find the quartiles.
The first quartile, , is 56 .
The second quartile, , is 62 .
The third quartile, , is 63 .
(Type integers or decimals.)

Ask by Rodriquez O'Quinn. in the United States

Jan 10,2025

UpStudy AI · Accepted Answer

Sure, let's continue with parts **b** and **c** based on your dataset and the quartiles you've identified.

### b. Find the Interquartile Range (IQR)

The **Interquartile Range (IQR)** is a measure of statistical dispersion and is calculated as the difference between the third quartile ($$ Q_{3} $$) and the first quartile ($$ Q_{1} $$).

$$
\text{IQR} = Q_{3} - Q_{1}
$$

Given:
- $$ Q_{1} = 56 $$
- $$ Q_{3} = 63 $$

$$
\text{IQR} = 63 - 56 = 7
$$

**Interquartile Range (IQR) = 7**

---

### c. Identify Any Outliers

Outliers are data points that fall significantly below or above the overall pattern of the data. To identify outliers, we can use the 1.5*IQR rule:

1. **Calculate the Lower Bound:**
   $$
   \text{Lower Bound} = Q_{1} - 1.5 \times \text{IQR} = 56 - 1.5 \times 7 = 56 - 10.5 = 45.5
   $$

2. **Calculate the Upper Bound:**
   $$
   \text{Upper Bound} = Q_{3} + 1.5 \times \text{IQR} = 63 + 1.5 \times 7 = 63 + 10.5 = 73.5
   $$

3. **Determine Outliers:**
   - Any data point **less than 45.5** or **greater than 73.5** is considered an outlier.

**Given Data Set:**
$$
58, 56, 62, 55, 54, 56, 59, 64, 63, 65, 58, 55, 58, 63, 81
$$

**Checking for Outliers:**
- The data point **81** is greater than **73.5**, so it is an outlier.

**Identified Outlier:**
- **81**

---

### Summary

- **Interquartile Range (IQR):** 7
- **Outlier Detected:** 81

If you have any further questions or need additional assistance, feel free to ask!
- **Interquartile Range (IQR):** 7 - **Outlier:** 81

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