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7.8
Activity
Unit
Activity
抽样分布（M&M豆和彩虹糖）
Sampling Distribution Experiment with M&M’s and Skittles
用M&M豆和彩虹糖进行抽样分布实验
Objective / 实验目的
- Understand and visualize the concept of sampling distribution.
- 掌握并直观感受抽样分布的概念。
Materials Needed / 所需材料
1. M&M’s candies (1 pack) 巧克力豆，不要买花生豆🥜
2. Skittles candies (1 pack)
3. Pen and paper for recording data
4. Calculator (optional)
5. Blank tables for sampling and distribution results
Steps / 操作步骤
Prepare the Data / 准备数据
- Count the number of each color in the pack of M&M’s (e.g., blue, orange, green, yellow, red, brown).
- Record the counts and calculate the proportion of each color.
- Repeat the same process for Skittles (e.g., orange, green, yellow, red, brown).
- 统计M&M豆中每种颜色的数量（如蓝色、橙色、绿色、黄色、红色和棕色）。
- 记录数量并计算每种颜色所占的比例。
- 同样统计彩虹糖的颜色数量（如橙色、绿色、黄色、红色和棕色）。
Sampling / 抽样过程
- Take a random sample of 15 candies from M&M’s. （n=15）
Spread out all your M&M’s, mix them around, then close your eyes or look away, and pick 15 candies at random. That’s your sample!
- Record the number of red candies in the sample $$x$$).
- Calculate the sample proportion of red candies ( $$P_{\text{red}} = \hat{p} = \frac{x}{n}$$).
- Take a random sample of 15 candies from Skittles.
- Record the number of red candies in the sample ($$x$$).
- Calculate the sample proportion of red candies ( $$P_{\text{red}} = \hat{p} = \frac{x}{n}$$).
- 从M&M豆中随机抽取15颗糖果：（n=15）
先把一整包 M&M’s 倒出来或放在桌面上，或者放在一个袋子里，搅一搅让它们混合得更均匀。然后闭上眼睛或者不看糖果，随机拿走15颗。这样就得到一个随机样本啦。
- 记录红色糖果的数量 $$x$$。
- 计算红色糖果的比例 ($$P_{\text{red}} = \hat{p} = \frac{x}{n}$$ )。
- 从彩虹糖中随机抽取15颗糖果：（n=15）
- 记录红色糖果的数量 $$x$$。
- 计算红色糖果的比例 ($$P_{\text{red}} = \hat{p} = \frac{x}{n}$$ )。
Construct Sampling Distributions / 构建抽样分布
- Repeat the sampling process multiple times (at least 10 for M&M’s and 10 for Skittles).
- Record the data in tables.
- Compute the average proportion for each dataset.
- 重复抽样过程（M&M豆和彩虹糖分别至少抽取10次）。
- 在表格中记录数据。
- 计算每组数据的平均比例 (把每次比例加起来，然后除以总次数！)
Tables / 数据记录表
M&M's 数据记录表:
Skittles 数据记录表:
次数 | X (红色糖果数量) | 红色糖果的比例$$P_{\text{red}} = \hat{p}$$ (%) |
1 | ㅤ | ㅤ |
2 | ㅤ | ㅤ |
3 | ㅤ | ㅤ |
4 | ㅤ | ㅤ |
5 | ㅤ | ㅤ |
ㅤ | ... | ... |
10 | ㅤ | ㅤ |
ㅤ | ㅤ | MEAN：把每次比例加起来，然后除以总次数！ |
次数 | X (红色糖果数量) | 红色糖果的比例$$P_{\text{red}} = \hat{p}$$ (%) |
1 | ㅤ | ㅤ |
2 | ㅤ | ㅤ |
3 | ㅤ | ㅤ |
4 | ㅤ | ㅤ |
5 | ㅤ | ㅤ |
ㅤ | ㅤ | ㅤ |
10 | ... | ... |
ㅤ | MEAN： | MEAN：把每次比例加起来，然后除以总次数！ |
Discussion / 讨论
- Analyze the differences in between M&M’s and Skittles.
- Observe the shape of the sampling distribution.
- 总结M&M豆和彩虹糖的的差异。
- 观察抽样分布的形状。
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