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The table displays the mean name length for seven samples of students.

Sample
Mean Name Length
1
5.4
2
7.1
3
6.3
4
5.2
5
6.0
6
4.9
7
6.2

What can be said about the variation between the sample means?
The variation between the sample means is small.
The variation between the sample means is large.
The variation shows that the values are far apart.
The variation cannot be used to make predictions.

1 answer

To analyze the variation between the sample means, we can look at the data provided:

  • Sample 1: 5.4
  • Sample 2: 7.1
  • Sample 3: 6.3
  • Sample 4: 5.2
  • Sample 5: 6.0
  • Sample 6: 4.9
  • Sample 7: 6.2

Calculating the range (highest mean - lowest mean):

  • Highest mean: 7.1 (Sample 2)
  • Lowest mean: 4.9 (Sample 6)
  • Range: 7.1 - 4.9 = 2.2

Given that the means range from 4.9 to 7.1, there is a noticeable difference between the highest and lowest samples.

Thus, we can conclude that the variation between the sample means is large, as there is a significant spread in the mean lengths reported across the samples. The statements "The variation shows that the values are far apart" and "The variation between the sample means is large" both adequately describe the situation, but the strongest and most straightforward choice would be:

The variation between the sample means is large.