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

Explanation:

Step1: Find the maximum and minimum values

The data set is (14, 13, 6, 6, 14, 13, 5). The maximum value (x_{max}=14) and the minimum value (x_{min}=5).

Step2: Calculate the range

The range (R) is given by the formula (R = x_{max}-x_{min}). So (R=14 - 5=9).

Step3: Calculate the mean (\bar{x})

(\bar{x}=\frac{14 + 13+6+6+14+13+5}{7}=\frac{71}{7}\approx10.14).

Step4: Calculate the squared - differences ((x_i-\bar{x})^2)

For (x_1 = 14): ((14 - 10.14)^2=(3.86)^2 = 14.8996) For (x_2 = 13): ((13 - 10.14)^2=(2.86)^2 = 8.1796) For (x_3 = 6): ((6 - 10.14)^2=(- 4.14)^2 = 17.1396) For (x_4 = 6): ((6 - 10.14)^2=(-4.14)^2 = 17.1396) For (x_5 = 14): ((14 - 10.14)^2=(3.86)^2 = 14.8996) For (x_6 = 13): ((13 - 10.14)^2=(2.86)^2 = 8.1796) For (x_7 = 5): ((5 - 10.14)^2=(-5.14)^2 = 26.4196) The sum of squared - differences (\sum_{i = 1}^{7}(x_i-\bar{x})^2=14.8996+8.1796 + 17.1396+17.1396+14.8996+8.1796+26.4196=106.8572).

Step5: Calculate the sample standard deviation (s)

The formula for the sample standard deviation is (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}), where (n = 7). (s=\sqrt{\frac{106.8572}{7 - 1}}=\sqrt{\frac{106.8572}{6}}\approx\sqrt{17.8095}\approx4.22).

Answer:

Range = 9 day(s) s = 4.22