The table below gives the percent of children under five considered to be underweight.
Percent of Underweight Children | Number of Countries |
---|---|
16.1-21.5 | 21 |
21.6-25.9 | 7 |
26.0-30.3 | 7 |
30.4-35.7 | 3 |
35.8-37.3 | 3 |
37.4-42.5 | 3 |
42.6-48.7 | 2 |
- What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)
- What is the standard deviation? (Round your answer to two decimal places.)
- Which interval(s) could be considered unusual? Explain.
- None of the intervals could be considered unusual since none of them contain any values in the range of ±2 standard deviations from the mean.
- The intervals 37.4-42.5 and 42.6-48.7 could be considered unusually high since they contain values that are at least two standard deviations above the mean percentage of underweight children.
- The interval 26.0-30.3 could be considered unusually high since it contains values that are at least two standard deviations above the mean percentage of underweight children.
- The interval 16.1-21.5 could be considered unusually low since it contains values that are at least two standard deviations below the mean percentage of underweight children.
1. Mean Calculation
To estimate the mean, we’ll use the midpoint for each interval, multiply it by the frequency of that interval, and then sum all the values and divide by the total number of countries.
Step 1: Find Midpoints
Step 2: Multiply Midpoints by Frequencies
Step 3: Calculate Mean
2. Standard Deviation Calculation
Step 1: Calculate (x−mean)2 for Each Interval
Step 2: Multiply by Frequency
Step 3: Sum and Divide by Total Frequency
3. Determine Unusual Intervals
We consider values more than two standard deviations away from the mean to determine if an interval is unusual.
Unusual Range:
Unusual Intervals:
Conclusion