Question

The following data was collected from 10 visitors to Disneyland. A researcher stood at the entrance gate and interviewed the first 10 families that agreed to participate. Each family was asked, “How many times have you been to Disneyland?” The data values were: 1, 1, 2, 2, 2, 2, 3, 3, 4, 7. The average number of visits was calculated and reported.
Calculate the standard deviation of the data values.

Answer 1

The standard deviation is $\sigma=1.676$

Step-by-step explanation:

The given data are $1,1,2,2,2,2,3,3,4,7$

Thus, $N=10$

The mean for the data is given by

$\begin{aligned}\mu &=\frac{\text {Sum of data}}{N} \\&=\frac{1+1+2+2+2+2+3+3+4+7}{10} \\&=\frac{27}{10} \\\mu &=2.7\end{aligned}$

The standard deviation is given by

$\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}$

Substituting the values in the formula and simplifying the equation,we get,

$=\sqrt{\frac{1}{10}(2.89+2.89+0.49+0.49+0.49+0.49+0.09+0.09+1.69+1.69+18.49)} =\sqrt{\frac{1}{10}(28.1)} =\sqrt{2.81} =1.676$Thus, the standard deviation for the data is $\sigma=1.676$