Question

Daily Calorie Consumption The five number summary for daily calorie consumption for the \(n=315\) participants in the NutritionStudy is \((445,\) 1334,1667,2106,6662) (a) Give the range and the IQR. (b) Which of the following numbers is most likely to be the mean of this dataset? Explain. $$ \begin{array}{llll} 1550 & 1667 & 1796 & 3605 \end{array} $$ (c) Which of the following numbers is most likely to be the standard deviation of this dataset? Explain. \(\begin{array}{lllll}5.72 & 158 & 680 & 1897 & 5315\end{array}\)

Short answer

The range and IQR of the dataset are 6217 and 772, respectively. The most probable mean of the dataset is 1667. The most likely standard deviation of the dataset is 680.

Step-by-step solution

Range Calculation

The range of a dataset is calculated by subtracting the smallest number from the largest number. In this instance, it would be \( 6662 - 445 \)

IQR Calculation

The interquartile range (IQR) is calculated by subtracting the first quartile from the third quartile. Here, it should be \( 2106 - 1334 \)

Mean Identification

The mean of a dataset is its 'center' or 'balance point'. The value should be somewhere in the middle of the data range. Considering the choices given, the number that appears to be in the middle of our range is the median, 1667, so that's most likely to be our mean.

Standard Deviation Identification

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. Considering the choices given and our calculated mean, the most suitable number is 680, which indicates a moderate level of variation.