Standard Deviation

In a grouped frequency table, the representative value used for each class in variance and standard deviation calculations is typically:

• The class boundary.

• The class midpoint.

• The median of the entire dataset.

• The mode of the entire dataset.

If a dataset’s standard deviation is very large, it implies:

• The data values are closely clustered around the mean.

• The data values are widely spread out from the mean.

• All values in the dataset are identical.

• The mean of the dataset is very small.

If the sample standard deviation of a dataset is s=0, this implies:

• There are at least two different values in the dataset.

• The mean of the dataset is negative.

• All data points are identical.

• The dataset is infinite.

One reason why variance and standard deviation from grouped data might differ slightly from the exact value using all raw data is:

• Class midpoints are only approximations of the actual data values within each class.

• Grouped data always adds 1 to the standard deviation.

• Frequency tables have no effect on variance calculations.

• Grouped data calculations always equal the ungrouped results exactly.

Which scenario best illustrates a real-world use of standard deviation?

• Counting how many items in a grocery list start with letter “C.”

• Determining how spread out daily sales figures are for a small business.

• Checking if the total frequency of data is 100%.

• Finding the sum of 10 random integers.

Which of these datasets is most likely to be grouped for standard deviation calculations due to its continuous nature?

• Number of siblings each student in class has (0, 1, 2, 3...).

• The color choices (red, blue, green) for a set of 30 students.

• The time (in seconds) it takes to run a 100-meter race

• A list of T-shirt sizes (S, M, L, XL).

• 60.815

• 66.45

• 70.1

• 73.5

• 0.8413

• 0.9772

• 0.9332

• 0.9082

• 84.13

• 86.51

• 92.07

• 95.45

A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. When the meter reads 1.00 L , the amount of fuel a certain pump dispenses is normally distributed with a mean of   1 L standard deviation of 0.05 L . Find the probability that amount dispensed in a random trial is less than or equal to 1.05 L.

• 0.16 %

• 16%

• 0.84%

• 84%