Questions: The following data set is the number of pounds of garbage that each household threw away in one week. 46, 12, 34, 11, 7, 13, 27, 39, 15, 36, 35, 11, 55, 18, 52, 17, 24, 37, 47, 54, 25, 23, 26, 11 a. Mean 28.125 b. Median 25.5 C. Mode 11 d. Range 44 e. Standard Deviation f. IQR 14 g. Upper Fence h. Lower Fence

Solution Steps

To solve the given questions, we need to calculate the mean, median, mode, range, standard deviation, interquartile range (IQR), upper fence, and lower fence for the provided data set. The mean, median, mode, and range are already given, so we will focus on calculating the standard deviation, IQR, upper fence, and lower fence.

1. Standard Deviation: Calculate the standard deviation using the formula for the sample standard deviation.
2. IQR (Interquartile Range): Calculate the first quartile (Q1) and the third quartile (Q3), then find the difference between Q3 and Q1.
3. Upper Fence: Calculate using the formula \( Q3 + 1.5 \times IQR \).
4. Lower Fence: Calculate using the formula \( Q1 - 1.5 \times IQR \).

The standard deviation is a measure of the amount of variation or dispersion in a set of values. For the given data set, the standard deviation is calculated as: \[ \text{Standard Deviation} = 15.11 \]

The interquartile range (IQR) is the difference between the third quartile (\(Q3\)) and the first quartile (\(Q1\)). For the given data set: \[ Q1 = 14.5 \] \[ Q3 = 37.5 \] \[ \text{IQR} = Q3 - Q1 = 37.5 - 14.5 = 23.0 \]

The upper fence is calculated using the formula: \[ \text{Upper Fence} = Q3 + 1.5 \times \text{IQR} \] Substituting the values: \[ \text{Upper Fence} = 37.5 + 1.5 \times 23.0 = 37.5 + 34.5 = 72.0 \]

The lower fence is calculated using the formula: \[ \text{Lower Fence} = Q1 - 1.5 \times \text{IQR} \] Substituting the values: \[ \text{Lower Fence} = 14.5 - 1.5 \times 23.0 = 14.5 - 34.5 = -20.0 \]

Final Answer