Question

here is a dotplot of the amount of fat (to the nearest gram) in 12 different hamburgers served at a fast - food restaurant. the distribution of fat content has a mean of $\bar{x}=22.83$ grams and a standard deviation of $s_x = 9.06$ grams.

choose the correct interpretation of the standard deviation.

there is a lot of variability in the fat content of the hamburgers from this restaurant.
standard deviation is calculated by finding the sum of the squared differences of each individual value and the mean. then, you divide by the sample size minus one. finally, take the square root.
$s_x=sqrt{\frac{sum(x_i - \bar{x})^2}{n - 1}}$
the fat content of these 12 hamburgers typically varies by about 9.06 grams from the mean of 22.83 grams.
you can expect the fat content of these 12 burgers to vary from 13.77 to 31.89 grams.

Explanation:

The standard deviation measures the amount of variation or dispersion of a set of values. A standard - deviation of 9.06 grams for the fat - content data means that, on average, the fat content of each hamburger typically varies by about 9.06 grams from the mean fat content of 22.83 grams. The first option just says there is a lot of variability without quantifying it precisely. The second option is the formula for calculating standard deviation, not an interpretation of the given value. The fourth option is about a range which is not the correct interpretation of standard deviation.

Answer:

The fat content of these 12 hamburgers typically varies by about 9.06 grams from the mean of 22.83 grams.