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.