Question
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): Skip to navigation
Answers
GPT-4o mini
To find the values such as range, outlier, median, lower quartile (Q1), upper quartile (Q3), and interquartile range (IQR) from the data set, I would need the specific values from Carol's study, typically presented in a table. However, I can explain how to calculate each of these values.
1. **Range**: The difference between the maximum and minimum values in the data set.
\[
\text{Range} = \text{Maximum} - \text{Minimum}
\]
2. **Outlier**: A value that lies outside 1.5 times the interquartile range below Q1 or above Q3. The steps to identify outliers are:
- Calculate IQR: \( \text{IQR} = Q3 - Q1 \)
- Calculate lower bound: \( Q1 - 1.5 \times \text{IQR} \)
- Calculate upper bound: \( Q3 + 1.5 \times \text{IQR} \)
- Any data point outside these bounds is considered an outlier.
3. **Median**: The middle value when the data set is ordered. If there's an even number of data points, the median is the average of the two middle numbers.
4. **Lower Quartile (Q1)**: The median of the first half of the data (below the median).
5. **Upper Quartile (Q3)**: The median of the second half of the data (above the median).
6. **Interquartile Range (IQR)**: The difference between the upper and lower quartiles.
\[
\text{IQR} = Q3 - Q1
\]
If you can provide the data set from Carol's study, I can help you compute these statistics.
1. **Range**: The difference between the maximum and minimum values in the data set.
\[
\text{Range} = \text{Maximum} - \text{Minimum}
\]
2. **Outlier**: A value that lies outside 1.5 times the interquartile range below Q1 or above Q3. The steps to identify outliers are:
- Calculate IQR: \( \text{IQR} = Q3 - Q1 \)
- Calculate lower bound: \( Q1 - 1.5 \times \text{IQR} \)
- Calculate upper bound: \( Q3 + 1.5 \times \text{IQR} \)
- Any data point outside these bounds is considered an outlier.
3. **Median**: The middle value when the data set is ordered. If there's an even number of data points, the median is the average of the two middle numbers.
4. **Lower Quartile (Q1)**: The median of the first half of the data (below the median).
5. **Upper Quartile (Q3)**: The median of the second half of the data (above the median).
6. **Interquartile Range (IQR)**: The difference between the upper and lower quartiles.
\[
\text{IQR} = Q3 - Q1
\]
If you can provide the data set from Carol's study, I can help you compute these statistics.