Data Analysis Notes and Worksheets - Lindsay Bowden - Free Printable

Let's go through the worksheet step by step and fill in the blanks, then answer the questions based on the histogram provided.

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Fill in the Blanks:

shape of data – tells us how the data is distributed
center of data – gives us the middle of the data set
*can be found by mean or median*

spread of data – tells how widely spread out or varied the data set is
*can be found by range, interquartile range, mean absolute deviation, or standard deviation*

peak – point where the data is higher than the other parts of the data set
*can be found by mode*
*one peak = unimodal*
*two peaks = bimodal*
*multiple peaks = multimodal*
*no peaks = uniform*

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Now, analyze the Histogram:

The histogram shows the number of students who read for different numbers of minutes each night. The x-axis is grouped into intervals (0–4, 5–9, ..., 30–34), and the y-axis shows the number of students.

#### 1. How would you describe the shape of the data?

Looking at the histogram:
- It has a single high bar at the 15–19 minute interval.
- The bars increase up to that point and then decrease symmetrically on both sides.
- The left and right sides are roughly mirror images.

✔ This is a symmetric, unimodal distribution, resembling a bell-shaped curve.

> ✔ Answer: The shape of the data is symmetric and unimodal (approximately bell-shaped).

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#### 2. How many peaks does the graph have?

There is one clear highest bar (at 15–19 minutes), which is higher than all others.

> ✔ Answer: The graph has one peak.

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#### 3. Estimate the center (mean or median) of this data set.

Since the distribution is symmetric, the mean and median are approximately equal and located at the peak of the distribution.

The peak is in the 15–19 minute interval.

So, we estimate the center to be around the middle of that interval:
→ $ \frac{15 + 19}{2} = 17 $ minutes

> ✔ Answer: The center is approximately 17 minutes.

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#### 4. How would you describe the spread of data?

Look at the range of the data:
- The data ranges from 0–4 to 30–34 minutes.
- Most students read between 5–29 minutes.
- The spread is relatively narrow, with most values clustered around the center.

We can say:
- The range is about 30–34 minutes minus 0–4 minutes → roughly 30–34 minutes wide.
- The interquartile range (IQR) would be from about 10–14 to 25–29 minutes (where most of the middle data lies).
- The data is moderately spread out, but not extremely variable.

> ✔ Answer: The spread of the data is moderate, with most students reading between 5 and 29 minutes. The data is fairly tightly clustered around the center.

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✔ Final Answers:

1. Shape of the data: Symmetric and unimodal (bell-shaped)
2. Number of peaks: One peak
3. Estimated center: Approximately 17 minutes
4. Spread of data: Moderate spread; most values cluster around the center, ranging from about 5 to 29 minutes.

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Let me know if you'd like help calculating exact measures like mean or IQR!