Answer :
To solve this question, we need to determine the mean absolute deviation (MAD) for each branch and compare them to understand the spread.
1. Calculate the mean absolute deviation for the West Avenue Branch:
- Given data points: [7, 9, 6, 11, 7, 9, 12, 10, 4]
- The mean (average) of these data points is calculated first.
- Next, we calculate the absolute deviation of each data point from the mean.
- Finally, we take the mean of these absolute deviations to get the MAD.
- The mean absolute deviation for the West Avenue Branch is 2.074074074074074.
2. Calculate the mean absolute deviation for the Water Field Road Branch:
- Given data points: [18, 20, 12, 15, 7, 6, 11, 13, 19]
- The mean (average) of these data points is calculated first.
- Next, we calculate the absolute deviation of each data point from the mean.
- Finally, we take the mean of these absolute deviations to get the MAD.
- The mean absolute deviation for the Water Field Road Branch is 4.049382716049383.
3. Compare the spreads of the two data sets:
- The MAD for the West Avenue Branch is 2.074074074074074.
- The MAD for the Water Field Road Branch is 4.049382716049383.
- Since 2.074074074074074 is less than 4.049382716049383, the spread of the data for the West Avenue Branch is less than the spread of the data for the Water Field Road Branch.
Based on this detailed step-by-step solution, we can fill in the blanks as follows:
- The mean absolute deviation of the data for the West Avenue Branch is 2.074074074074074.
- The mean absolute deviation of the data for the Water Field Road Branch is 4.049382716049383.
- Based on the mean absolute deviations for the two data sets, we can conclude that the spread of the data for the West Avenue Branch is less than the spread of the data for the Water Field Road Branch.
1. Calculate the mean absolute deviation for the West Avenue Branch:
- Given data points: [7, 9, 6, 11, 7, 9, 12, 10, 4]
- The mean (average) of these data points is calculated first.
- Next, we calculate the absolute deviation of each data point from the mean.
- Finally, we take the mean of these absolute deviations to get the MAD.
- The mean absolute deviation for the West Avenue Branch is 2.074074074074074.
2. Calculate the mean absolute deviation for the Water Field Road Branch:
- Given data points: [18, 20, 12, 15, 7, 6, 11, 13, 19]
- The mean (average) of these data points is calculated first.
- Next, we calculate the absolute deviation of each data point from the mean.
- Finally, we take the mean of these absolute deviations to get the MAD.
- The mean absolute deviation for the Water Field Road Branch is 4.049382716049383.
3. Compare the spreads of the two data sets:
- The MAD for the West Avenue Branch is 2.074074074074074.
- The MAD for the Water Field Road Branch is 4.049382716049383.
- Since 2.074074074074074 is less than 4.049382716049383, the spread of the data for the West Avenue Branch is less than the spread of the data for the Water Field Road Branch.
Based on this detailed step-by-step solution, we can fill in the blanks as follows:
- The mean absolute deviation of the data for the West Avenue Branch is 2.074074074074074.
- The mean absolute deviation of the data for the Water Field Road Branch is 4.049382716049383.
- Based on the mean absolute deviations for the two data sets, we can conclude that the spread of the data for the West Avenue Branch is less than the spread of the data for the Water Field Road Branch.
