Questions: In 2022, Antarctica recorded record-breaking high temperatures. Consider the monthly average temperature (in degrees Celsius) for 2021 displayed in the table. -15.7, -21.9, -30.4, -35.4, -30.6, -29.7, -30.5, -39.8, -35.5, -28.9, -20.6, -16.5 Use the stats tool to find the mean and standard deviation of the temperature data. Round answers to 2 decimal places. The mean is and the standard deviation is

Solution Steps

To find the mean temperature, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of observations and \( x_i \) are the temperature values. For our data:

\[ \sum_{i=1}^{12} x_i = -335.5 \quad \text{and} \quad N = 12 \]

Thus, the mean temperature is calculated as:

\[ \mu = \frac{-335.5}{12} = -27.96 \]

The variance is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} \]

Substituting the values, we find:

\[ \sigma^2 = 54.02 \]

The standard deviation is the square root of the variance:

\[ \sigma = \sqrt{\sigma^2} = \sqrt{54.02} \approx 7.35 \]

Final Answer