a study recorded the time it took for a sample of seven different species of frogs and toads eggs to hatch…

Explanation:

Step1: Find maximum and minimum

The data set is (7, 10, 13, 10, 13, 7, 5). The maximum value (max = 13) and the minimum value (min=5).

Step2: Calculate the range

The formula for the range (R) of a data - set is (R = max - min). So (R=13 - 5=8).

Step3: Calculate the mean

The mean (\bar{x}=\frac{7 + 10+13+10+13+7+5}{7}=\frac{65}{7}\approx9.286).

Step4: Calculate the squared differences

((7 - 9.286)^2\approx(- 2.286)^2 = 5.226), ((10 - 9.286)^2\approx(0.714)^2 = 0.51), ((13 - 9.286)^2\approx(3.714)^2 = 13.794), ((10 - 9.286)^2\approx0.51), ((13 - 9.286)^2\approx13.794), ((7 - 9.286)^2\approx5.226), ((5 - 9.286)^2\approx(-4.286)^2 = 18.37).

Step5: Calculate the sum of squared differences

(S=\sum_{i = 1}^{n}(x_i-\bar{x})^2=5.226+0.51 + 13.794+0.51+13.794+5.226+18.37=57.43).

Step6: Calculate the sample variance

The formula for the sample variance (s^2=\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}), where (n = 7). So (s^2=\frac{57.43}{6}\approx9.572).

Step7: Calculate the sample standard deviation

The sample standard deviation (s=\sqrt{s^2}=\sqrt{9.572}\approx3.1).

Answer:

Range = 8 days, Sample standard deviation (\approx3.1) days