Question

1. if a data set has q1 = 15 and an iqr of 10, what is the upper bound for outliers?

a. 30
b. 20
c. 40
d. 15

Explanation:

Step1: Find Q3

We know that \( \text{IQR} = Q3 - Q1 \). Given \( Q1 = 15 \) and \( \text{IQR} = 10 \), we can solve for \( Q3 \):
\( Q3 = Q1 + \text{IQR} = 15 + 10 = 25 \).

Step2: Calculate the upper bound for outliers

The formula for the upper bound (UB) for outliers is \( \text{UB} = Q3 + 1.5 \times \text{IQR} \).
Substitute \( Q3 = 25 \) and \( \text{IQR} = 10 \):
\( \text{UB} = 25 + 1.5 \times 10 = 25 + 15 = 40 \). Wait, no—wait, did I mix up Q1 and Q3? Wait, no, the upper bound is \( Q3 + 1.5 \times \text{IQR} \), but first we need Q3. Wait, no, wait: Wait, IQR is \( Q3 - Q1 \), so \( Q3 = Q1 + IQR = 15 + 10 = 25 \). Then upper bound is \( 25 + 1.5 \times 10 = 25 + 15 = 40 \)? But let's check again. Wait, maybe I made a mistake. Wait, no, the formula for outliers: lower bound is \( Q1 - 1.5 \times IQR \), upper bound is \( Q3 + 1.5 \times IQR \). So first, find Q3: \( Q3 = Q1 + IQR = 15 + 10 = 25 \). Then upper bound: \( 25 + 1.5 \times 10 = 25 + 15 = 40 \). So the upper bound is 40. Wait, but let's check the options. Option c is 40. Wait, but maybe I messed up. Wait, no, let's re-express:

Wait, no, wait: Wait, the question is about upper bound for outliers. The formula is \( \text{Upper Bound} = Q3 + 1.5 \times \text{IQR} \). But we need Q3. Since \( \text{IQR} = Q3 - Q1 \), then \( Q3 = Q1 + \text{IQR} = 15 + 10 = 25 \). Then \( \text{Upper Bound} = 25 + 1.5 \times 10 = 25 + 15 = 40 \). So the answer should be 40, which is option c. Wait, but let's confirm. Wait, maybe I made a mistake in Q3. Wait, no, IQR is Q3 - Q1, so Q3 is Q1 + IQR. So 15 + 10 is 25. Then upper bound is 25 + 15 = 40. So the correct answer is 40, which is option c. Wait, but let's check the options again. The options are a. 30, b. 20, c. 40, d. 15. So yes, 40 is option c.

Answer:

c. 40