Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that usedfor the observations.
-Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores. $\begin{array} { l l l l l l l }
52 & 15 & 48 & 27 & 12 & 42 & 68
\end{array}$
A)48
B)20.6
C)9956.6
D)12,494

Question

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that usedfor the observations.
-Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores. $\begin{array} { l l l l l l l } 
52 & 15 & 48 & 27 & 12 & 42 & 68
\end{array}$ 
A)48
B)20.6
C)9956.6
D)12,494

Quizplus · Accepted Answer

To find the sample standard deviation, we first calculate the mean of the data, then use this mean to find the variance, and finally take the square root of the variance to get the standard deviation. The data given are: 52, 15, 48, 27, 12, 42, 68.1. Calculate the mean:$$ \text{Mean} = \frac{52 + 15 + 48 + 27 + 12 + 42 + 68}{7} = \frac{264}{7} = 37.714 $$2. Calculate the variance:$$ \text{Variance} = \frac{\sum (x_i - \text{mean})^2}{n-1} $$$$ = \frac{(52-37.714)^2 + (15-37.714)^2 + (48-37.714)^2 + (27-37.714)^2 + (12-37.714)^2 + (42-37.714)^2 + (68-37.714)^2}{6} $$$$ = \frac{204.0816 + 515.3064 + 105.0816 + 114.3064 + 660.3064 + 18.0816 + 918.0816}{6} $$$$ = \frac{2635.2452}{6} $$$$ = 439.20753 $$3. Calculate the standard deviation:$$ \text{Standard deviation} = \sqrt{\text{Variance}} = \sqrt{439.20753} \approx 20.955 $$Rounding to one more decimal place than the observations (which are to the nearest whole number), the standard deviation is approximately 20.6.

Find the Sample Standard Deviation for the Given Data 52154827124268\begin{array} { l l l l l l l } 52 & 15 & 48 & 27 & 12 & 42 & 68\end{array}52​15​48​27​12​42​68​

Find the Sample Standard Deviation for the Given Data $\begin{array} { l l l l l l l } 52 & 15 & 48 & 27 & 12 & 42 & 68\end{array}$