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I see the image you uploaded is from a statistics worksheet or textbook page focusing on frequency distributions and multiple-choice questions. I'll help break down each of the questions and their solutions.

### Solutions:
1. **Question 1:**
   - You're given the following frequency table with \( N = \_\_\_\_\):

     | X  | f  |
     |----|----|
     | 4  | 2  |
     | 3  | 4  |
     | 2  | 2  |

     To find \( N \), sum the frequencies:

     \[
     N = 2 + 4 + 2 = 8
     \]

     **Answer:** \( N = 8 \)

2. **Question 2:**
   - You're asked how many individuals had a score of \( X = 2 \). From the table, when \( X = 2 \), the frequency is 2, meaning 2 individuals had this score.

     **Answer:** \( 2 \)

3. **Question 3:**
   - You're given the following table and asked to find \( \Sigma X \):

     | X  | f  |
     |----|----|
     | 4  | 1  |
     | 3  | 2  |
     | 1  | 2  |

     To find \( \Sigma X \), you multiply each value of \( X \) by its corresponding frequency, then sum the results:

     \[
     \Sigma X = (4 \times 1) + (3 \times 2) + (1 \times 2) = 4 + 6 + 2 = 12
     \]

     **Answer:** \( \Sigma X = 12 \)

4. **Question 4:**
   - You're given that the scores range from a high of \( X = 67 \) to a low of \( X = 23 \) and asked how many intervals would be needed if the interval width is 5 points.

     First, find the range:

     \[
     \text{Range} = 67 - 23 = 44
     \]

     Then, divide the range by the interval width:

     \[
     \frac{\text{Range}}{\text{Interval Width}} = \frac{44}{5} \approx 8.8
     \]

     Since you can't have a fraction of an interval, round up to the nearest whole number.

     **Answer:** \( \text{around } 9 \)

Would you like more details on any specific part? Here are some relative questions you might find useful:

1. How do you construct a frequency distribution table from raw data?
2. What is the importance of calculating the cumulative frequency?
3. How do you determine the appropriate interval width for grouped data?
4. What is the difference between a frequency polygon and a bar graph?
5. How do skewed distributions affect the interpretation of data?

**Tip:** When creating frequency tables, always ensure that the sum of frequencies \( f \) matches the total sample size \( N \).

Solutions to multiple-choice questions based on frequency distributions from a statistics worksheet.

Explore detailed solutions to a statistics worksheet involving frequency distributions, including calculating total frequency, sum of weighted frequencies, and determining the number of intervals in grouped data. Suitable for college students studying introductory statistics.

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