Answer :
Final answer:
The mean height of the whole group comprising 13 boys and 12 girls, with boys having a mean height of 1.69 m and girls 1.62 m, is calculated to be approximately 1.66 m.
Explanation:
To find the mean height of the whole group of 13 boys and 12 girls, we calculate the total height for each group and then divide by the total number of students. The mean height is the sum of all the heights divided by the number of individuals. We have the following information:
- Number of boys (nb) = 13
- Mean height of boys (mb) = 1.69 m
- Number of girls (ng) = 12
- Mean height of girls (mg) = 1.62 m
First, we calculate the total height of the boys (Tb) and the total height of the girls (Tg):
Tb = nb × mb = 13 × 1.69 m = 21.97 m
Tg = ng × mg = 12 × 1.62 m = 19.44 m
The total number of students is nb + ng = 13 + 12 = 25.
To get the total height of all students, we add Tb and Tg:
Total height (T) = Tb + Tg = 21.97 m + 19.44 m = 41.41 m
Finally, to find the mean height of the group (M), we divide the total height by the total number of students:
M = T / (nb + ng) = 41.41 m / 25 = 1.6564 m
Therefore, the mean height of the whole group is approximately 1.66 m.
