Question: User: As the new manager of a small convenience store, you want to understand the shopping patterns of your customers. You randomly sample 20 purchases from yesterdays records. The amounts of those purchases (in dollars) are shown.
Complete parts a) through d).
38.71 3.27 32.14 46.29
37.53 33.74 63.54 50.34
56.99 81.97 47.88 11.01
21.73 40.53 37.79 31.92
94.71 74.97 46.64 65.79
a) Is the distribution unimodal or multimodal?
The distribution is unimodal.
b) Where is(are) the mode(s)?
A. The modes of the data are around $10 and $90.
B. The mode of the data is around $50.
C. The mode of the data is around $30.
D. The modes of the data are around $0 and $100.
Graph: a histogram at center-left shows purchase amounts on the x-axis from 0 to 100 and number of purchases on the y-axis from 0 to 10, with a single main peak around $40 60 and smaller bars near $0 20 and $80 100.anwser this for me
1. **State the problem:** We are given 20 purchase amounts and asked to determine if the distribution is unimodal or multimodal and identify the mode(s).
2. **Understanding modes:** The mode is the value or values that appear most frequently in a data set. A distribution is unimodal if it has one clear peak (one mode), and multimodal if it has multiple peaks (multiple modes).
3. **Analyze the data:** The purchase amounts are:
$$38.71, 3.27, 32.14, 46.29, 37.53, 33.74, 63.54, 50.34, 56.99, 81.97, 47.88, 11.01, 21.73, 40.53, 37.79, 31.92, 94.71, 74.97, 46.64, 65.79$$
4. **Look at the histogram description:** It shows a single main peak around $40$ to $60$, with smaller bars near $0$ to $20$ and $80$ to $100$.
5. **Conclusion on modality:** Since there is one main peak, the distribution is **unimodal**.
6. **Identify the mode(s):** The main peak is around $40$ to $60$, which corresponds to option B: "The mode of the data is around $50$."
**Final answer:**
- a) The distribution is unimodal.
- b) The mode of the data is around $50$ (Option B).