Question

the following data points represent the number of hours each of the staff members at daniels department store slept thanksgiving night. answer 2 questions about the data set. 1. sort the data from least to greatest. 2.6 3 4.9 5 5 6 6 7.9 8 8.2 2. find the interquartile range (iqr) of the data set.

Explanation:

Step1: Determine the median

The data set has 10 values. The median is the average of the 5th and 6th - ordered values. Since the 5th value is 5 and the 6th value is 6, the median $Q_2=\frac{5 + 6}{2}=5.5$.

Step2: Find the lower half and $Q_1$

The lower - half of the data set is $\{2.6,3,4.9,5,5\}$. The median of the lower - half ($Q_1$) is the 3rd value, so $Q_1 = 4.9$.

Step3: Find the upper half and $Q_3$

The upper - half of the data set is $\{6,6,7.9,8,8.2\}$. The median of the upper - half ($Q_3$) is the 3rd value, so $Q_3=7.9$.

Step4: Calculate the IQR

The inter - quartile range is $IQR = Q_3−Q_1$. Substitute $Q_1 = 4.9$ and $Q_3 = 7.9$ into the formula: $IQR=7.9 - 4.9=3$.

Answer:

1. $2.6,3,4.9,5,5,6,6,7.9,8,8.2$
2. $3$