The responses of a sample of 5313 shoppers who were asked how their purchases are made are shown in the table. Find the​ mean, the​ median, and the mode of the​ data, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why.
How Purchases Are Made
​Frequency, f
 
Research online and in​ store, buy in store
2276
Search and buy online
1113
Search and buy in store
890
Research online and in​ store, buy online
1034
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Part 1
Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The mean is 
  
enter your response here.
​(Round to one decimal place as​ needed.)
B.
The mean cannot be calculated because the sample size is too small.
C.
The mean cannot be calculated because the data are at the nominal level of measurement.
D.
The mean cannot be calculated because there is an even number of data entries.

### Step 1: Identify the correct type of data
The data represents categorical responses (how purchases are made), with frequencies for each category. Since this data is **nominal** (descriptive categories with no inherent numerical order), calculating the **mean** is inappropriate because mean is a measure for numerical data.

### Answer for the Mean:
The correct answer is:
**C. The mean cannot be calculated because the data are at the nominal level of measurement.**

---

### Part 2: Find the median
The median is the middle value in a data set when the data is arranged in order. However, since this is categorical data (nominal), the **median** cannot be calculated because there is no order or ranking in the categories.

### Answer for the Median:
The median cannot be calculated due to the nominal level of the data.

---

### Part 3: Find the mode
The **mode** is the value (or category) that appears most frequently in a data set. In this case, the mode represents the category with the highest frequency.

From the data### Step 1: Identify the correct type of data
The data represents categorical responses (how purchases are made), with frequencies for each category. Since this data is **nominal** (descriptive categories with no inherent numerical order), calculating the **mean** is inappropriate because mean is a measure for numerical data.

### Answer for the Mean:
The correct answer is:
**C. The mean cannot be calculated because the data are at the nominal level of measurement.**

---

### Part 2: Find the median
The median is the middle value in a data set when the data is arranged in order. However, since this is categorical data (nominal), the **median** cannot be calculated because there is no order or ranking in the categories.

### Answer for the Median:
The median cannot be calculated due to the nominal level of the data.

---

### Part 3: Find the mode
The **mode** is the value (or category) that appears most frequently in a data set. In this case, the mode represents the category with the highest frequency.

From the 
- Research online and in-store, buy in-store: 2276
- Search and buy online: 1113
- Search and buy in-store: 890
- Research online and in-store, buy online: 1034

The mode is **"Research online and in-store, buy in-store"**, as it has the highest frequency (2276).

---

### Conclusion:
- **Mean:** Cannot be calculated (nominal data)
- **Median:** Cannot be calculated (nominal data)
- **Mode:** "Research online and in-store, buy in-store" (frequency = 2276)

---

Would you like more details or have any questions about this? Here are some related questions:

1. What is the difference between nominal, ordinal, interval, and ratio data?
2. Can we calculate any measures of central tendency for nominal data other than mode?
3. How would you calculate the mean, median, and mode for ordinal or interval data?
4. What is the purpose of calculating the mode for nominal data?
5. How can we visualize nominal data effectively?

**Tip:** Mode is the only central tendency measure valid for nominal data since it indicates the most frequent category, not a numerical average.

The responses of a sample of 5313 shoppers who were asked how their purchases are made are shown in the table. Find the​ mean, the​ median, and the mode of the​ data, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why.

Analyze the shopper purchase data from a sample of 5313 shoppers, understanding how to find the mode in nominal data. This example highlights why the mean and median cannot be calculated for nominal data and emphasizes the importance of mode as a measure of central tendency in this context.

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