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

Explanation:

Step1: Calculate the mean

The data set is (7, 10, 13, 10, 13, 7, 5). The mean (\bar{x}=\frac{7 + 10+13+10+13+7+5}{7}=\frac{65}{7}\approx9.29).

Step2: Calculate the squared - differences

For (x_1 = 7): ((7 - 9.29)^2=(- 2.29)^2 = 5.2441) For (x_2 = 10): ((10 - 9.29)^2=(0.71)^2 = 0.5041) For (x_3 = 13): ((13 - 9.29)^2=(3.71)^2 = 13.7641) For (x_4 = 10): ((10 - 9.29)^2=(0.71)^2 = 0.5041) For (x_5 = 13): ((13 - 9.29)^2=(3.71)^2 = 13.7641) For (x_6 = 7): ((7 - 9.29)^2=(-2.29)^2 = 5.2441) For (x_7 = 5): ((5 - 9.29)^2=(-4.29)^2 = 18.4041)

Step3: Calculate the sum of squared - differences

(\sum_{i = 1}^{7}(x_i-\bar{x})^2=5.2441+0.5041 + 13.7641+0.5041+13.7641+5.2441+18.4041=57.4327)

Step4: Calculate the sample variance

The sample variance (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}), where (n = 7). So (s^2=\frac{57.4327}{7 - 1}=\frac{57.4327}{6}\approx9.5721)

Step5: Calculate the sample standard deviation

The sample standard deviation (s=\sqrt{s^2}=\sqrt{9.5721}\approx3.10)

Answer:

3.10