49
50
50
50
55
55
75
95
100
105
175
175
225
234
250
250
275
325
350
375
375
375
375
2500
3000
Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the data and then​ (e) answer the given question.

Let's break this down step by step.

### Given Data:
49, 50, 50, 50, 55, 55, 75, 95, 100, 105, 175, 175, 225, 234, 250, 250, 275, 325, 350, 375, 375, 375, 375, 2500, 3000

### (a) **Mean**:
The mean is the average of the data points, calculated as the sum of all the values divided by the number of values.

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]

### (b) **Median**:
The median is the middle value when the data points are arranged in ascending order. If there is an even number of data points, the median is the average of the two middle values.

### (c) **Mode**:
The mode is the value that appears most frequently in the dataset.

### (d) **Midrange**:
The midrange is calculated as the average of the maximum and minimum values.

\[
\text{Midrange} = \frac{\text{Maximum value} + \text{Minimum value}}{2}
\]

### (e) **Answer the Given Question**:
This will depend on what the question specifically asks. If it relates to interpretation (e.g., which measure best represents the data), we can discuss it after calculating the above statistics.

Let me calculate these values for you.Here are the results for the given data set:

### (a) **Mean**: 
The mean is approximately \( 397.72 \).

### (b) **Median**: 
The median is \( 225 \), as it is the middle value in the sorted data.

### (c) **Mode**: 
The mode is \( 375 \), as it appears the most frequently in the data set.

### (d) **Midrange**: 
The midrange is \( 1524.5 \), calculated as the average of the minimum value \( 49 \) and the maximum value \( 3000 \).

Would you like to further discuss any of these values or answer a specific question about the data?

### Here are 5 related questions:
1. How does the presence of extreme values (like 2500 and 3000) affect the mean?
2. Is the median a better measure of central tendency for this data than the mean? Why?
3. Why do you think 375 appears most frequently in this data set?
4. What could be the significance of the midrange being quite high compared to the mean and median?
5. What is the range of this data set, and how could it influence data interpretation?

### Tip:
When a dataset contains outliers or extreme values, the median is often a better representation of central tendency than the mean.

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Data: 49, 50, 50, 50, 55, 55, 75, 95, 100, 105, 175, 175, 225, 234, 250, 250, 275, 325, 350, 375, 375, 375, 375, 2500, 3000.

Solve a data analysis problem involving a dataset with extreme values (49, 50, 50, ..., 3000). Learn how to calculate mean, median, mode, and midrange, and understand how these statistics are affected by the presence of outliers.

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