A researcher wants to compare the mean scores of students from three different educational programs: Agric Education, Business Education, and Industrial Technical Education. The scores are provided be

Agric Education (Group 1): Scores (X1) = 7, 6, 6, 4, 8, 3, 6, 5, 7, 4

• Number of observations ($n_1$) = 10
• Sum ($T_1$) = $7+6+6+4+8+3+6+5+7+4 = 56$
• Mean ($\bar{X}_1$) = $\frac{56}{10} = 5.6$
• Sum of squares ($\sum X_1^2$) = $7^2+6^2+6^2+4^2+8^2+3^2+6^2+5^2+7^2+4^2 = 336$

Business Education (Group 2): Scores (X2) = 5, 4, 5, 6, 3, 5, 4, 7, 3, 4

• Number of observations ($n_2$) = 10
• Sum ($T_2$) = $5+4+5+6+3+5+4+7+3+4 = 46$
• Mean ($\bar{X}_2$) = $\frac{46}{10} = 4.6$
• Sum of squares ($\sum X_2^2$) = $5^2+4^2+5^2+6^2+3^2+5^2+4^2+7^2+3^2+4^2 = 230$

Industrial Technical Education (Group 3): Scores (X3) = 8, 5, 6, 9, 7, 8, 9, 5, 6, 8

• Number of observations ($n_3$) = 10
• Sum ($T_3$) = $8+5+6+9+7+8+9+5+6+8 = 71$
• Mean ($\bar{X}_3$) = $\frac{71}{10} = 7.1$
• Sum of squares ($\sum X_3^2$) = $8^2+5^2+6^2+9^2+7^2+8^2+9^2+5^2+6^2+8^2 = 525$