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Suppose the following data are obtained by recording $X$, the number of customers that arrive at an automatic banking machine during $15$ successive one-minute time intervals.

2 1 3 2 0 1 4 2
0 2 3 1 0 0 4

The formula for sample variance is given by

$$s^2 = \frac{1}{n-1}\sum_{i=1}^{n} (x_i - \bar{x})$$

where $\bar{x} = 25/15$

I got $$\frac{1}{14}\left[(2-25/15)^2 + (1-25/15)^2 + (3-25/15)^2 \\ {}+ (2-25/15)^2 + (1-25/15)^2 + (4-25/15)^2 \\ {}+ (2-25/15)^2 + (2-25/15)^2 + (3-25/15)^2 \\ {}+ (1-25/15)^2 + (4-25/15)^2\right] \approx 1.15$$

whereas the answer is $1.94$ . What am I doing wrong here?

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You left out the points with value $0$, they do contribute to the variance because the mean is not zero.

When you do it right, you get $$\frac1{14}\frac{246}{9} \approx 1.952$$

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You are missing all the $(0 - \bar{x})^2$ components in the sum.

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