What is the range of this set of data? 111, 97, 63, 84, 100, 119, 72
The Correct Answer and Explanation is:
To find the range of a set of data, we use the formula:
[
\text{Range} = \text{Maximum value} – \text{Minimum value}
]
Step 1: Identify the Maximum and Minimum Values
- The data set is: 111, 97, 63, 84, 100, 119, 72
- First, arrange the data in ascending order: [
63, 72, 84, 97, 100, 111, 119
] - The maximum value is the largest number in the set, which is 119.
- The minimum value is the smallest number in the set, which is 63.
Step 2: Calculate the Range
Now that we know the maximum and minimum values, we can subtract the minimum value from the maximum value to find the range:
[
\text{Range} = 119 – 63 = 56
]
Final Answer:
The range of the data set is 56.
Explanation of the Range:
The range of a data set represents the difference between the highest and lowest values, giving an indication of how spread out the values are. A larger range suggests that the data is more spread out, while a smaller range indicates that the values are more concentrated around the center.
In this case, the range of 56 shows that the data points vary significantly. The smallest value, 63, and the largest value, 119, are quite far apart, suggesting a moderate spread in the data set.
The range is a simple measure of variability but does not tell us anything about the distribution or any potential outliers beyond the extreme values. For more detailed insights, other statistical measures such as the interquartile range or standard deviation could be used to describe the spread and variability of the data more precisely.