a) Data Collection for Variable(s)

The data are the scores of students on a test, which represents one variable (test scores).

Yes, it is appropriate to make a stem-and-leaf plot for this type of data. Stem-and-leaf plots are especially useful for displaying small to medium datasets where you want to retain the original data values but still see the distribution. Given that you have 20 scores, this plot will give you a clear picture of the data spread.

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b) Complete the Stem-and-Leaf Plot

You are asked to fill in the stem-and-leaf plot with the tens place as the stem and the ones place as the leaf. Here’s how we can do that:

Data: 59, 52, 65, 90, 78, 55, 56, 52, 63, 84, 52, 65, 64, 71, 66, 61, 98, 84, 68, 59, 76, 77, 65, 52, 56, 50, 77, 70.

We first sort the data for clarity:

50, 52, 52, 52, 55, 56, 56, 59, 59, 61, 63, 64, 65, 65, 65, 66, 68, 70, 71, 76, 77, 77, 78, 84, 84, 84, 90, 98.

Now, let's organize it:

• 5: 0, 2, 2, 2, 5, 6, 6, 9, 9
• 6: 1, 3, 4, 5, 5, 6, 8
• 7: 0, 1, 6, 7, 7
• 8: 4, 4, 4
• 9: 0, 8

Stem-and-Leaf Plot:

Stems   Leaves
5       0, 2, 2, 2, 5, 6, 6, 9, 9
6       1, 3, 4, 5, 5, 6, 8
7       0, 1, 6, 7, 7
8       4, 4, 4
9       0, 8

Key: 9 | 8 means a score of 98.

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c) Shape of the Distribution

The shape of the distribution based on this stem-and-leaf plot appears to be roughly symmetric with a slight right skew (positively skewed). There are a few high values (90, 98) but most of the data is concentrated around the 50s, 60s, and 70s. The distribution shows a tendency for scores to cluster in the lower to middle range, with fewer students achieving high scores.

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Summary of Answers:

• a) Data were collected for one variable (test scores).
• b) Stem-and-leaf plot completed above.
• c) The shape is slightly right-skewed.

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Do you need any further clarification on the stem-and-leaf plot or any other part of this?

Additional Related Questions:

1. How do you interpret a right-skewed distribution?
2. What other ways can you visualize the shape of this data?
3. What other statistical measures can describe the distribution (e.g., mean, median)?
4. How would this data change if we added more students with higher scores?
5. Why might a stem-and-leaf plot be more helpful than a histogram for this data?

Tip: Remember that stem-and-leaf plots maintain the actual data values, so they can provide more detailed insight into the distribution compared to other graphical representations.