Answer:
Therefore, the best estimate for the mean percentage of underweight children is approximately 31.92%.
Explanation:
To determine the best estimate for the mean percentage of underweight children, we can use the midpoint of each interval provided in Table 2.76. Let's calculate the mean using the midpoints:
1. The midpoint of the first interval (16-21.45) is:
(16 + 21.45) / 2 = 18.725
2. The midpoint of the second interval (21.45-26.9) is:
(21.45 + 26.9) / 2 = 24.175
3. The midpoint of the third interval (26.9-32.35) is:
(26.9 + 32.35) / 2 = 29.625
4. The midpoint of the fourth interval (32.35-37.8) is:
(32.35 + 37.8) / 2 = 35.075
5. The midpoint of the fifth interval (37.8-43.25) is:
(37.8 + 43.25) / 2 = 40.525
6. The midpoint of the sixth interval (43.25-48.7) is:
(43.25 + 48.7) / 2 = 45.975
Now, we can calculate the mean by finding the average of these midpoints:
(18.725 + 24.175 + 29.625 + 35.075 + 40.525 + 45.975) / 6 ≈ 31.92
Therefore, the best estimate for the mean percentage of underweight children is approximately 31.92%.
To calculate the standard deviation, we need to use the formula and the midpoints. Since we are given the frequencies of each interval in Table 2.76, we can consider each frequency as the number of data points falling within that interval.