Question

grace is looking at a report of her monthly cell - phone usage for the last year to determine if she needs to upgrade her plan. the list represents the approximate number of megabytes of data grace used each month. 700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750. what is the standard deviation of the data? round to the nearest whole number. 65 75 100 130

Explanation:

Step1: Calcular la media

La media $\bar{x}=\frac{700 + 735+680 + 890+755+740+670+785+805+1050+820+750}{12}=\frac{9280}{12}\approx773.33$.

Step2: Calcular las diferencias al cuadrado

$(700 - 773.33)^2\approx5377.78$, $(735 - 773.33)^2\approx1469.44$, $(680 - 773.33)^2\approx8710.89$, $(890 - 773.33)^2\approx13626.78$, $(755 - 773.33)^2\approx336.11$, $(740 - 773.33)^2\approx1110.89$, $(670 - 773.33)^2\approx10676.89$, $(785 - 773.33)^2\approx136.11$, $(805 - 773.33)^2\approx992.78$, $(1050 - 773.33)^2\approx76544.44$, $(820 - 773.33)^2\approx2187.78$, $(750 - 773.33)^2\approx544.44$.

Step3: Calcular la varianza

La varianza $s^{2}=\frac{5377.78+1469.44 + 8710.89+13626.78+336.11+1110.89+10676.89+136.11+992.78+76544.44+2187.78+544.44}{12 - 1}=\frac{121618.64}{11}\approx11056.24$.

Step4: Calcular la desviación estándar

La desviación estándar $s=\sqrt{11056.24}\approx105.15\approx100$ (redondeado al entero más cercano).

Answer:

100