To calculate the mean height and standard deviation of the given data, we'll follow these steps:

Given Data:

Heights (in meters): 1.42, 1.35, 1.37, 1.50, 1.38, 1.30

(i) Mean Height

The mean height is calculated by summing all the heights and then dividing by the number of data points.

$\text{Mean Height} = \frac{1.42 + 1.35 + 1.37 + 1.50 + 1.38 + 1.30}{6}$

$\text{Mean Height} = \frac{7.32}{6} = 1.22$

(ii) Standard Deviation of the Heights

The standard deviation (SD) is calculated using the following formula:

$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$

where:

• $x_i$ are the individual data points,
• $\bar{x}$ is the mean of the data,
• $n$ is the number of data points.

1. First, find the differences from the mean for each height:

1.42 - 1.22 & = 0.20 \\ 1.35 - 1.22 & = 0.13 \\ 1.37 - 1.22 & = 0.15 \\ 1.50 - 1.22 & = 0.28 \\ 1.38 - 1.22 & = 0.16 \\ 1.30 - 1.22 & = 0.08 \\ \end{align*}$$ 2. Square each of these differences: $$\begin{align*} (0.20)^2 & = 0.04 \\ (0.13)^2 & = 0.0169 \\ (0.15)^2 & = 0.0225 \\ (0.28)^2 & = 0.0784 \\ (0.16)^2 & = 0.0256 \\ (0.08)^2 & = 0.0064 \\ \end{align*}$$ 3. Sum these squared differences: $$\text{Sum of Squared Differences} = 0.04 + 0.0169 + 0.0225 + 0.0784 + 0.0256 + 0.0064 = 0.19$$ 4. Divide by $$n - 1$$ (since it's a sample standard deviation): $$\frac{0.19}{5} = 0.038$$ 5. Finally, take the square root to find the standard deviation: $$s = \sqrt{0.038} \approx 0.1949$$ ### Final Answers: (i) The mean height is **1.22 meters**. (ii) The standard deviation of the heights is approximately **0.1949 meters**. Do you want more details or have any questions? Here are 5 related questions: 1. How would the mean height change if another child with a height of 1.45 meters were added? 2. Why is it important to use $$n - 1$$ in the calculation of sample standard deviation? 3. How would the standard deviation change if all the heights were increased by 0.1 meters? 4. Can the standard deviation ever be negative? 5. What does the standard deviation tell you about the distribution of the heights? **Tip:** Always double-check your calculations when working with standard deviation, as even small errors in squaring or summing can lead to significant differences.