a statistics student gave a survey to students which asked how many first cousins they have. the data from…

a statistics student gave a survey to students which asked how many first cousins they have. the data from the first nine responses are shown below. 6, 2, 7, 8, 8, 8, 5, 10, 10. what is the standard deviation of the data? 2.38 first cousins 2.52 first cousins 5.65 first cousins 6.36 first cousins

a statistics student gave a survey to students which asked how many first cousins they have. the data from the first nine responses are shown below. 6, 2, 7, 8, 8, 8, 5, 10, 10. what is the standard deviation of the data? 2.38 first cousins 2.52 first cousins 5.65 first cousins 6.36 first cousins

Answer

Explanation:

Step1: Calcular la media

La media $\bar{x}=\frac{6 + 2+7 + 8+8+8+5+10+10}{9}=\frac{64}{9}\approx7.11$.

Step2: Calcular la desviación de cada valor

$(6 - 7.11)^2=(- 1.11)^2 = 1.2321$, $(2 - 7.11)^2=(-5.11)^2 = 26.1121$, $(7 - 7.11)^2=(-0.11)^2 = 0.0121$, $(8 - 7.11)^2=(0.89)^2 = 0.7921$, $(8 - 7.11)^2=(0.89)^2 = 0.7921$, $(8 - 7.11)^2=(0.89)^2 = 0.7921$, $(5 - 7.11)^2=(-2.11)^2 = 4.4521$, $(10 - 7.11)^2=(2.89)^2 = 8.3521$, $(10 - 7.11)^2=(2.89)^2 = 8.3521$.

Step3: Calcular la varianza

La varianza $s^{2}=\frac{1.2321+26.1121 + 0.0121+0.7921+0.7921+0.7921+4.4521+8.3521+8.3521}{9 - 1}=\frac{51.89}{8}=6.48625$.

Step4: Calcular la desviación estándar

La desviación estándar $s=\sqrt{6.48625}\approx2.52$.

Answer:

2.52 first cousins