**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.

This answer was edited.## 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

$Mean=\frac{\sum (f\times x)}{\sum f}\backslash text\{Mean\}\; =\; \backslash frac\{\backslash sum\; (f\; \backslash times\; x)\}\{\backslash sum\; f\}$ $Mean=\frac{394.8+166.25+197.05+99.15+109.65+119.85+91.3}{21+7+7+3+3+3+2}\backslash text\{Mean\}\; =\; \backslash frac\{394.8\; +\; 166.25\; +\; 197.05\; +\; 99.15\; +\; 109.65\; +\; 119.85\; +\; 91.3\}\{21\; +\; 7\; +\; 7\; +\; 3\; +\; 3\; +\; 3\; +\; 2\}$ $Mean=\frac{1177.05}{46}\approx 25.59\backslash text\{Mean\}\; =\; \backslash frac\{1177.05\}\{46\}\; \backslash approx\; 25.59$

## 2. Standard Deviation Calculation

## Step 1: Calculate $(x-mean{)}^{2}(x\; \u2013\; \backslash text\{mean\})^2$(x−mean)2 for Each Interval

## Step 2: Multiply by Frequency

## Step 3: Sum and Divide by Total Frequency

$Variance=\frac{\sum (f\times (x-mean{)}^{2})}{\sum f}\backslash text\{Variance\}\; =\; \backslash frac\{\backslash sum\; (f\; \backslash times\; (x\; \u2013\; \backslash text\{mean\})^2)\}\{\backslash sum\; f\}$ $Variance=\frac{2992.00}{46}\approx 65.04\backslash text\{Variance\}\; =\; \backslash frac\{2992.00\}\{46\}\; \backslash approx\; 65.04$ $StandardDeviation=\sqrt{65.04}\approx 8.06$

## 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

Mean Percentage of Underweight Children:25.59Standard Deviation:8.06Unusual Intervals: