Problem 6
Question
In Exercises 1-6, find the range for each group of data items. \(3,3,3,4,5,5,5\)
Step-by-Step Solution
Verified Answer
The range of the given data set is 2.
1Step 1: Identify the highest and lowest values
In the given data set \(3,3,3,4,5,5,5\), the highest value is 5 and the lowest value is 3.
2Step 2: Calculate the range
The range is found by subtracting the lowest value from the highest value. Therefore, the range for this data set is \(5-3 = 2\).
Key Concepts
Finding RangeHighest and Lowest ValuesCalculating Range
Finding Range
The range in statistics is a simple, yet important concept that measures the spread or dispersion of a data set. To find the range, you need to first understand what it represents. The range is the difference between the highest and lowest values in a data set. This difference gives us an idea about how much variation or spread there is in the data.
Finding the range can be very useful in analyzing variations in data. It helps to quickly assess how wide or narrow a data set is distributed. This is particularly helpful when you are comparing different sets of data to see which one has more variation.
Finding the range can be very useful in analyzing variations in data. It helps to quickly assess how wide or narrow a data set is distributed. This is particularly helpful when you are comparing different sets of data to see which one has more variation.
Highest and Lowest Values
When calculating the range, it is crucial to correctly identify the highest and lowest values within your data set. Consider the example data set of\(3, 3, 3, 4, 5, 5, 5\).
- Highest value: This is the largest number in the data set. In our example, the highest value is 5.
- Lowest value: This is the smallest number in the data set. In our example, the lowest value is 3.
Calculating Range
Once you have identified the highest and lowest values in your data set, calculating the range becomes straightforward. Use the formula for range:
\(\text{Range} = \text{Highest Value} - \text{Lowest Value}\)
Applying this to our example, where the highest value is 5 and the lowest value is 3, the calculation of the range is as follows:
This calculation helps quantify the variance in your data, providing a quick snapshot of its total spread or dispersion.
\(\text{Range} = \text{Highest Value} - \text{Lowest Value}\)
Applying this to our example, where the highest value is 5 and the lowest value is 3, the calculation of the range is as follows:
- Subtract the lowest value from the highest value: \(5 - 3 = 2\).
This calculation helps quantify the variance in your data, providing a quick snapshot of its total spread or dispersion.
Other exercises in this chapter
Problem 5
A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been i
View solution Problem 6
In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=-0.4\)
View solution Problem 6
A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been i
View solution Problem 7
In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=-1.2\)
View solution