To complete this table, we need to calculate the missing values $A$, $B$, and $C$. Here's the approach:

Step 1: Determine Observed Count $A$

The total observed count for all categories is 130. Since counts for categories 2, 3, and 4 are given (37, 36, and 23 respectively), we can find $A$ by subtracting these from the total:

$A = 130 - (37 + 36 + 23) = 130 - 96 = 34$

Step 2: Determine Expected Count $B$

The expected counts are calculated based on the percentages given for each age group. For category 3 (22-24), the expected count $B$ is based on 30% of the total sample of 130 students:

$B = 0.30 \times 130 = 39$

Step 3: Determine Chi-Squared Value $C$

The chi-squared statistic for each category is calculated as:

$\chi^2 = \frac{(O - E)^2}{E}$

where $O$ is the observed count, and $E$ is the expected count. To find $C$, which is the chi-squared value for the fourth category:

$C = \frac{(23 - 26)^2}{26} = \frac{9}{26} = 0.346$

Summary of Values

1. A (Observed Count for category 1): $A = 34$
2. B (Expected Count for category 3): $B = 39.000$
3. C (Chi-squared for category 4): $C = 0.346$

Would you like more detailed explanations on chi-squared calculations?

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Further Questions to Explore:

1. What does the chi-squared value represent in this context?
2. How does changing sample size affect the chi-squared value?
3. Why is the expected count derived from percentage distributions?
4. How would the result change if observed counts differed slightly?
5. What conclusion could be drawn from a high total chi-squared value?

Tip:

When calculating expected counts, always ensure they are proportional to the sample size and distribution percentages.