https://r2.erweima.ai/mathbot/image/17261654721331jobe0dr.jpg

Let's analyze the data given in the image step-by-step to answer the questions. 

### Data Overview
The table presents information about 14 individuals, including the number of friends, gender, and age group (whether they are younger or older than 30).

### Given Data
- **Number of Friends**: [1052, 250, 153, 77, 89, 558, 669, 997, 2523, 47, 93, 390, 107, 930]
- **Gender**: Male or Female
- **Age Group**: Age ≤ 30 or Age ≥ 30

### Step-by-Step Solutions

1. **Find the mode (modal number) of friends.**
   - The mode is the most frequent number in the dataset.
   - Since all values are unique, there is no mode.

2. **Find the median number of friends.**
   - To find the median, arrange the values in ascending order: [47, 77, 89, 93, 107, 153, 250, 390, 558, 669, 930, 997, 1052, 2523].
   - The median is the middle value. Since there are 14 values, the median is the average of the 7th and 8th values: \((250 + 390) / 2 = 320\).

3. **Find the mean (average) number of friends.**
   - Mean = (Sum of all values) / (Number of values)
   - Sum = 1052 + 250 + 153 + 77 + 89 + 558 + 669 + 997 + 2523 + 47 + 93 + 390 + 107 + 930 = 6936
   - Mean = 6936 / 14 ≈ 495.43

4. **Find the range of friends.**
   - Range = Maximum value - Minimum value
   - Range = 2523 - 47 = 2476

5. **Indicate one common observation about the data.**
   - There is a wide variation in the number of friends, ranging from as low as 47 to as high as 2523.

### Additional Questions
1. How does the average number of friends differ between males and females?
2. What percentage of the individuals have more than 500 friends?
3. Are there any outliers in the number of friends, and how would removing them affect the average?
4. What is the distribution of ages in terms of friend counts?
5. Is there a trend or correlation between age and the number of friends?

### Tip
When analyzing data, identifying and removing outliers can help in understanding the central tendency of the dataset more accurately.

Los siguientes datos muestran la información personal de 14 personas, incluyendo su edad, sexo y número de amigos en redes sociales. Encuentra el número modal de amigos, la mediana, la media, el rango, y otras observaciones clave sobre los datos.

Analyze the friend count data from 14 individuals to find key statistical measures like mode, median, mean, and range. This problem explores descriptive statistics and data analysis concepts, suitable for high school students.

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