Suppose, we have 10 observations such that 39, 46, 44, 30, 73, 96, 91, 115, 112, 89. How many outliers are there?

To identify outliers in a data set using the Inter Quartile Range (IQR) method, follow these steps:

1. **Calculate the IQR:**
   From the previous calculation, we know:
   \[
   Q1 = 44, \quad Q3 = 96, \quad IQR = 52
   \]

2. **Determine the lower and upper bounds:**
   - Lower bound: \( Q1 - 1.5 \times IQR \)
   - Upper bound: \( Q3 + 1.5 \times IQR \)

   \[
   \text{Lower bound} = 44 - 1.5 \times 52 = 44 - 78 = -34
   \]
   \[
   \text{Upper bound} = 96 + 1.5 \times 52 = 96 + 78 = 174
   \]

3. **Identify outliers:**
   Any data points below the lower bound or above the upper bound are considered outliers.

   Given the data set:
   \[
   30, 39, 44, 46, 73, 89, 91, 96, 112, 115
   \]

   - All data points are above -34.
   - All data points are below 174.

Since all data points fall within the range of -34 to 174, there are no outliers in this data set.

Would you like further details or have any questions?

Here are 5 numbered questions for you to ask next:
1. How do you calculate the z-score for a data point?
2. What are the properties of a normal distribution?
3. How do you perform a linear regression analysis?
4. Can you explain the concept of a p-value in hypothesis testing?
5. How do you construct a confidence interval for a mean?

Tip: Identifying outliers can help in understanding the variability in your data and in making more accurate statistical inferences.

Learn how to identify outliers in a dataset using the Inter Quartile Range (IQR) method. This problem involves calculating quartiles, determining the IQR, and applying upper and lower bounds to detect outliers. Suitable for advanced high school students studying statistics.

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