The height of five children are as follows: \( 61 \mathrm{~cm}, 70 \mathrm{~cm}, 54 \mathrm{~cm}, 81 \mathrm{~cm} \), and 42 cm . \( M=61.6 \mathrm{~cm} ; S D=13.3 \mathrm{~cm} \) What percentage of children have heights between 61.6 cm and 74.9 cm

To find the percentage of children with heights between \( 61.6 \, \text{cm} \) and \( 74.9 \, \text{cm} \), we will follow these steps: 1. **List the heights of the children**: - \( 61 \, \text{cm} \) - \( 70 \, \text{cm} \) - \( 54 \, \text{cm} \) - \( 81 \, \text{cm} \) - \( 42 \, \text{cm} \) 2. **Identify the heights that fall within the specified range**: - We need to check which of the heights are between \( 61.6 \, \text{cm} \) and \( 74.9 \, \text{cm} \). 3. **Count the number of children within the range**: - Heights in the range: - \( 61 \, \text{cm} \) (not included since it's less than \( 61.6 \, \text{cm} \)) - \( 70 \, \text{cm} \) (included) - \( 54 \, \text{cm} \) (not included) - \( 81 \, \text{cm} \) (not included) - \( 42 \, \text{cm} \) (not included) Thus, only \( 70 \, \text{cm} \) is within the range. 4. **Calculate the percentage**: - Total number of children = 5 - Number of children within the range = 1 (only \( 70 \, \text{cm} \)) The percentage can be calculated using the formula: \[ \text{Percentage} = \left( \frac{\text{Number of children in range}}{\text{Total number of children}} \right) \times 100 \] Substituting the values: \[ \text{Percentage} = \left( \frac{1}{5} \right) \times 100 \] Now, let's calculate the percentage. \[ \text{Percentage} = \left( \frac{1}{5} \right) \times 100 = 20\% \] Thus, **20% of the children have heights between \( 61.6 \, \text{cm} \) and \( 74.9 \, \text{cm} \)**.