Question
Mrs. Hall 35
Mr. Benny 45
Mr. Leggo 26
Ms. Talle 32
Miss Flower 46
Mrs. Gomez 38
Mrs. Range 39
Ms. Book 40
Mr. Toledo 26
Mr. Rich 72
Carol did a study to look at the number of television viewers who watched nightly news in various classes in her school. The results are shown in the table.
(6 points)
Find each listed value.
Range:
Outlier:
Median:
Lower quartile (Q1):
Upper quartile (Q3):
Interquartile range (IQR):
Mr. Benny 45
Mr. Leggo 26
Ms. Talle 32
Miss Flower 46
Mrs. Gomez 38
Mrs. Range 39
Ms. Book 40
Mr. Toledo 26
Mr. Rich 72
Carol did a study to look at the number of television viewers who watched nightly news in various classes in her school. The results are shown in the table.
(6 points)
Find each listed value.
Range:
Outlier:
Median:
Lower quartile (Q1):
Upper quartile (Q3):
Interquartile range (IQR):
Answers
GPT-4o mini
To analyze the data provided and find the requested values, let's start by organizing the ages in numerical order:
**Ages:**
- 26 (Mr. Leggo)
- 26 (Mr. Toledo)
- 32 (Ms. Talle)
- 35 (Mrs. Hall)
- 38 (Mrs. Gomez)
- 39 (Mrs. Range)
- 40 (Ms. Book)
- 45 (Mr. Benny)
- 46 (Miss Flower)
- 72 (Mr. Rich)
### Step 1: Find the Range
The range is calculated as the difference between the maximum and minimum values.
\[
\text{Range} = \text{Maximum} - \text{Minimum} = 72 - 26 = 46
\]
### Step 2: Identify Outliers
To identify outliers, we typically calculate the upper and lower bounds using the interquartile range (IQR).
First, we need to find Q1 and Q3.
### Step 3: Calculate Median
Since there are 10 values, the median is the average of the 5th and 6th values.
\[
\text{Median} = \frac{38 + 39}{2} = 38.5
\]
### Step 4: Calculate Q1 (Lower Quartile)
Q1 is the median of the first half of the data (the lower 5 values: 26, 26, 32, 35, 38).
\[
Q1 = 32
\]
### Step 5: Calculate Q3 (Upper Quartile)
Q3 is the median of the second half of the data (the upper 5 values: 39, 40, 45, 46, 72).
\[
Q3 = 45
\]
### Step 6: Calculate the Interquartile Range (IQR)
The IQR is calculated as follows:
\[
IQR = Q3 - Q1 = 45 - 32 = 13
\]
### Step 7: Identify Outliers
Outliers can be identified using the IQR:
1. Calculate the lower bound:
\[
Q1 - 1.5 \times IQR = 32 - 1.5 \times 13 = 32 - 19.5 = 12.5
\]
2. Calculate the upper bound:
\[
Q3 + 1.5 \times IQR = 45 + 1.5 \times 13 = 45 + 19.5 = 64.5
\]
Any value below 12.5 or above 64.5 is considered an outlier.
From our data:
- The only value that is greater than 64.5 is 72 (Mr. Rich), which is an outlier.
### Final Results:
- **Range:** 46
- **Outlier:** 72
- **Median:** 38.5
- **Lower Quartile (Q1):** 32
- **Upper Quartile (Q3):** 45
- **Interquartile Range (IQR):** 13
**Ages:**
- 26 (Mr. Leggo)
- 26 (Mr. Toledo)
- 32 (Ms. Talle)
- 35 (Mrs. Hall)
- 38 (Mrs. Gomez)
- 39 (Mrs. Range)
- 40 (Ms. Book)
- 45 (Mr. Benny)
- 46 (Miss Flower)
- 72 (Mr. Rich)
### Step 1: Find the Range
The range is calculated as the difference between the maximum and minimum values.
\[
\text{Range} = \text{Maximum} - \text{Minimum} = 72 - 26 = 46
\]
### Step 2: Identify Outliers
To identify outliers, we typically calculate the upper and lower bounds using the interquartile range (IQR).
First, we need to find Q1 and Q3.
### Step 3: Calculate Median
Since there are 10 values, the median is the average of the 5th and 6th values.
\[
\text{Median} = \frac{38 + 39}{2} = 38.5
\]
### Step 4: Calculate Q1 (Lower Quartile)
Q1 is the median of the first half of the data (the lower 5 values: 26, 26, 32, 35, 38).
\[
Q1 = 32
\]
### Step 5: Calculate Q3 (Upper Quartile)
Q3 is the median of the second half of the data (the upper 5 values: 39, 40, 45, 46, 72).
\[
Q3 = 45
\]
### Step 6: Calculate the Interquartile Range (IQR)
The IQR is calculated as follows:
\[
IQR = Q3 - Q1 = 45 - 32 = 13
\]
### Step 7: Identify Outliers
Outliers can be identified using the IQR:
1. Calculate the lower bound:
\[
Q1 - 1.5 \times IQR = 32 - 1.5 \times 13 = 32 - 19.5 = 12.5
\]
2. Calculate the upper bound:
\[
Q3 + 1.5 \times IQR = 45 + 1.5 \times 13 = 45 + 19.5 = 64.5
\]
Any value below 12.5 or above 64.5 is considered an outlier.
From our data:
- The only value that is greater than 64.5 is 72 (Mr. Rich), which is an outlier.
### Final Results:
- **Range:** 46
- **Outlier:** 72
- **Median:** 38.5
- **Lower Quartile (Q1):** 32
- **Upper Quartile (Q3):** 45
- **Interquartile Range (IQR):** 13