Given this data, what is the range of the average word lengths? Is the variation between sample means large or small?
Answer (2)
Range is 2.6 , Variation is small.
Explanation
Understand the problem and provided data We are given a table of 8 students and their corresponding mean word lengths. The mean word lengths are: 7.1, 4.5, 6.9, 5.2, 5.0, 4.7, 6.1, 4.5
Identify maximum and minimum values First, we need to identify the maximum and minimum mean word lengths from the given data.
Find the maximum The maximum mean word length is 7.1.
Find the minimum The minimum mean word length is 4.5.
Calculate the range The range is calculated by subtracting the minimum value from the maximum value: R an g e = M a x im u m − M inim u m = 7.1 − 4.5 = 2.6
Assess the variation Now, we need to assess whether the variation between the sample means is large or small. Since the range is 2.6, which is a relatively small value compared to the mean word lengths, we can say that the variation is small.
Final Answer The range of the average word lengths is 2.6, and the variation between sample means is small.
Examples
Understanding the range of average word lengths can be useful in various real-life scenarios. For example, in education, it can help teachers assess the reading complexity of different texts and match them to students' reading levels. In marketing, it can help copywriters tailor their messages to specific audiences with varying levels of literacy. In linguistics, it can provide insights into the vocabulary diversity and complexity of different languages or dialects. The range gives a quick measure of the spread of the data, which can inform decisions in these fields.
The range of the average word lengths is calculated to be 2.6, indicating the difference between the longest and shortest average word lengths. The variation between sample means is assessed to be small due to this relatively low range. This suggests that the average word lengths among the samples are closely similar to each other.
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