Let's solve each question based on the histograms provided for
Cat Owners and
Dog Owners, using the shape of data concepts shown at the top of the page.
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1. What is the shape for the cat owner histogram?
Looking at the
Cat Owners histogram:
- The bars increase from 0–1 (1 owner), to 2–3 (2 owners), then 4–5 (3 owners), peak at 6–7 (4 owners), and drop to 8+ (2 owners).
- The distribution has a
longer tail on the right (higher number of cats), with most people owning 6–7 cats.
- The peak is on the
left side, and the data trails off to the right.
✔ This is a
skewed right (positive skew) distribution.
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Answer: Skewed Right (Positive Skew)
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2. What is the shape of the dog owner histogram?
Looking at the
Dog Owners histogram:
- The bars go: 0–1 (2 owners), 2–3 (3 owners), 4–5 (4 owners), 6–7 (3 owners), 8+ (2 owners).
- The highest bar is in the
4–5 category, and the frequencies are fairly balanced on both sides.
- There’s no long tail on either side — it peaks in the middle and decreases symmetrically.
✔ This appears to be
symmetric or nearly symmetric.
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Answer: Symmetric
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3. How do the spread of the two data sets compare?
-
Spread refers to how far the data extends across the range.
- Both histograms have the same categories: 0–1, 2–3, 4–5, 6–7, 8+.
- Both data sets cover the
same range (from 0–1 up to 8+), so they have
similar spreads.
- However, the
distribution of values differs — Cat owners are more concentrated toward higher numbers, while Dog owners are more evenly distributed around the center.
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Answer: The spreads are similar because both data sets cover the same range of pet counts (0–1 to 8+).
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4. How do their peaks compare?
- The
peak is the highest bar in each histogram.
-
Cat Owners: Peak is at
6–7 cats (4 owners).
-
Dog Owners: Peak is at
4–5 dogs (4 owners).
- Both have the
same height (4 owners), but occur at different values.
- So, the
mode (most common value) is
6–7 cats vs.
4–5 dogs.
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Answer: Both histograms have peaks of the same height (4 owners), but the peak for cat owners occurs at a higher number of pets (6–7 cats) compared to dog owners (4–5 dogs).
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✔ Final Answers:
1.
Skewed Right
2.
Symmetric
3.
The spreads are similar; both cover the same range of pet counts.
4.
Both have peaks of the same height (4 owners), but the cat owner peak is at 6–7 cats, while the dog owner peak is at 4–5 dogs.
Let me know if you'd like a visual explanation or help interpreting box plots too!
Parent Tip: Review the logic above to help your child master the concept of algebra functions and data analysis worksheet.
