Data Analysis Notes and Worksheets - Lindsay Bowden - Free Printable

Let's solve the problem step by step, based on the image provided. This worksheet is about describing the shape, center, and spread of data using a histogram.

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🔹 First: Fill in the Blanks (Definitions)

1. Shape of data – tells us how the data is distributed
2. Center of data – gives us the middle of the data set
→ *can be found by mean or median*
3. Spread of data – tells how spread out or varied the data set is
→ *can be found by range, interquartile range, mean absolute deviation, or standard deviation*
4. 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.

#### Data Categories:
- X-axis: # of minutes (grouped into intervals)
- Y-axis: # of students

Intervals and frequencies:
- 0–4 min: 2 students
- 5–9 min: 4 students
- 10–14 min: 5 students
- 15–19 min: 6 students ← highest bar
- 20–24 min: 5 students
- 25–29 min: 4 students
- 30–34 min: 2 students

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❓ Questions & Answers:

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

✔ The histogram is symmetric and unimodal.

- It has one clear peak at 15–19 minutes.
- The bars rise to the peak and then decrease symmetrically on both sides.
- The left and right sides are roughly mirror images.

👉 So, the shape is approximately symmetric with a single peak.

> ✔ Answer: The shape of the data is symmetric and unimodal.

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

✔ There is one peak — at the 15–19 minute interval (height = 6).

> ✔ Answer: The graph has one peak.

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

We don’t have exact values, but we can estimate.

- The peak is at 15–19 minutes, which suggests the mode is around there.
- Since the distribution is symmetric, the mean and median should be close to the center of the peak.

So, the center is likely around 17 minutes (midpoint of 15–19).

> ✔ Answer: The center is approximately 17 minutes.

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

- The data ranges from 0–4 minutes to 30–34 minutes.
- Most students read between 5 and 29 minutes.
- The spread is moderate — not too wide, but covers a reasonable range.
- We can say the data is clustered around the center, with fewer students at the extremes.

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

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✔ Final Summary:

| Question | Answer |
|--------|--------|
| Shape of data | Symmetric and unimodal |
| Number of peaks | One peak |
| Estimated center | About 17 minutes |
| Spread of data | Moderate, clustered around the center |

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📝 Additional Notes:

- Symmetric means the left and right sides of the histogram are similar.
- Unimodal means one peak (most frequent value).
- In symmetric distributions, mean ≈ median.
- Spread refers to how much the data varies — here, it’s not very spread out.

Let me know if you'd like help calculating actual mean or median with assumed midpoint values!