Question

Calculate the values below of the following data.
{14, 14, 17, 18, 20, 21, 22, 24, 25, 47}
Q1 = BLANK
Q3 = BLANK
Interquartile Range (IQR) = BLANK
Values lower than BLANK and higher than BLANK are considered ourliers.
The outlier in this data set is BLANK

Answer 1

To calculate the quartiles and interquartile range (IQR), first, let's arrange the data in ascending order (the data is already sorted):

{14, 14, 17, 18, 20, 21, 22, 24, 25, 47}

**Step 1: Calculate Q1 and Q3**

1. **Find Q1 (1st Quartile):**
Q1 is the median of the first half of the data. The first half of the data set is {14, 14, 17, 18, 20}.
The median of this subset is the third value (since there are 5 values):
Q1 = 17.

2. **Find Q3 (3rd Quartile):**
Q3 is the median of the second half of the data. The second half of the data set is {21, 22, 24, 25, 47}.
The median of this subset is the third value:
Q3 = 24.

**Step 2: Calculate IQR**

IQR = Q3 - Q1 = 24 - 17 = 7.

**Step 3: Identify potential outliers**

To identify outliers, we use the 1.5 * IQR rule:

- Lower bound = Q1 - 1.5 * IQR = 17 - 1.5 * 7 = 17 - 10.5 = 6.5.
- Upper bound = Q3 + 1.5 * IQR = 24 + 1.5 * 7 = 24 + 10.5 = 34.5.

Values lower than 6.5 and higher than 34.5 are considered outliers.

**Identifying the outlier in the data set**:
The only value in the data set that is greater than 34.5 is 47.

**Final Output:**

Q1 = 17
Q3 = 24
Interquartile Range (IQR) = 7
Values lower than 6.5 and higher than 34.5 are considered outliers.
The outlier in this data set is 47.