Questions: The number of cookies that Jane ate during each of the last five days is as follows: 0,1,4,7,8. Rounded to the nearest tenth, the standard deviation of the number of cookies eaten daily is

Solution Steps

The mean \( \mu \) of the number of cookies eaten is calculated using the formula:

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

where \( N \) is the number of days and \( x_i \) represents the number of cookies eaten each day. For Jane's data:

\[ \mu = \frac{0 + 1 + 4 + 7 + 8}{5} = \frac{20}{5} = 4.0 \]

The variance \( \sigma^2 \) is calculated using the formula:

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

Substituting the values:

\[ \sigma^2 = \frac{(0 - 4)^2 + (1 - 4)^2 + (4 - 4)^2 + (7 - 4)^2 + (8 - 4)^2}{5} \]

Calculating each term:

\[ = \frac{16 + 9 + 0 + 9 + 16}{5} = \frac{50}{5} = 10.0 \]

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{\sigma^2} = \sqrt{10.0} \approx 3.1623 \]

Rounding to one decimal place gives:

\[ \sigma \approx 3.2 \]

Final Answer