Final answer:
The estimated mean percentage of children with the medical condition is 32.35%, calculated by averaging the midpoints of the given intervals. This mean percentage represents an improvement over the previous recovery rate of 25%.
Step-by-step explanation:
To estimate the mean percentage of children with the specified medical condition based on the given data, you can calculate the midpoint for each interval and then take the average of these midpoints. For each percentage range, identify the midpoint by adding the lower bound and upper bound and then dividing by 2.
After finding the midpoints, sum them all and divide by the total number of intervals to find the mean percentage. Assuming the intervals are evenly distributed and represent the entire range of the data, this would give us a reasonable estimate for the mean.
Below is the calculation for each interval group:
- (16 + 21.45) / 2 = 18.725
- (21.45 + 26.9) / 2 = 24.175
- (26.9 + 32.35) / 2 = 29.625
- (32.35 + 37.8) / 2 = 35.075
- (37.8 + 43.25) / 2 = 40.525
- (43.25 + 48.7) / 2 = 45.975
The mean percentage is calculated as follows:
(18.725 + 24.175 + 29.625 + 35.075 + 40.525 + 45.975) / 6 = 32.35%.
The mean percentage of children with the condition in the study is 32.35%, which is higher than the previous recovery rate of 25%. This suggests an improvement in the recovery rate compared to past data.