The job coordinator at Martin Luther King Magnet School surveyed 16-year old students on their hourly wages (in $) for their part-time jobs:
7.75, 8.00, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00, 10.00, 10.00, 10.25, 10.50, 10.75
Which measure of variability—IQR or MAD—best describes the spread of the dataset? Enter 1 for IQR or 2 for MAD.
(1 point)
3 answers
1
The job coordinator at Martin Luther King Magnet School surveyed 16-year old students on their hourly wages (in $) for their part-time jobs:
7.75, 8.00, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00, 10.00, 10.00, 10.25, 10.50, 10.75
Which measure of variability—IQR or MAD—best describes the spread of the dataset? Enter 1 for IQR or 2 for MAD.
(1 point).
7.75, 8.00, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00, 10.00, 10.00, 10.25, 10.50, 10.75
Which measure of variability—IQR or MAD—best describes the spread of the dataset? Enter 1 for IQR or 2 for MAD.
(1 point).
To determine which measure of variability best describes the spread of the dataset, we can compare the values of the interquartile range (IQR) and the mean absolute deviation (MAD).
The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the dataset. It provides a measure of the dispersion of the middle 50% of the data.
The MAD is the average of the absolute differences between each data point and the mean of the dataset. It provides a measure of the average distance of individual data points from the mean.
In this case, the dataset is relatively small, and the values are already sorted. We can calculate the IQR and MAD to compare which measure of variability best describes the spread of the dataset.
Calculating the IQR:
Q1 = 9.00
Q3 = 10.50
IQR = Q3 - Q1 = 10.50 - 9.00 = 1.50
Calculating the MAD:
Mean = (7.75 + 8.00 + 8.25 + 8.50 + 8.50 + 8.75 + 9.00 + 9.25 + 9.50 + 10.00 + 10.00 + 10.00 + 10.25 + 10.50 + 10.75) / 15 = 9.39
MAD = (|7.75 - 9.39| + |8.00 - 9.39| + |8.25 - 9.39| + |8.50 - 9.39| + |8.50 - 9.39| + |8.75 - 9.39| + |9.00 - 9.39| + |9.25 - 9.39| + |9.50 - 9.39| + |10.00 - 9.39| + |10.00 - 9.39| + |10.00 - 9.39| + |10.25 - 9.39| + |10.50 - 9.39| + |10.75 - 9.39|) / 15
= 0.71
When comparing the IQR with the MAD, we can see that the IQR is larger (1.50) than the MAD (0.71).
Therefore, the measure of variability that best describes the spread of the dataset is the IQR (1).
Answer: 1
The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the dataset. It provides a measure of the dispersion of the middle 50% of the data.
The MAD is the average of the absolute differences between each data point and the mean of the dataset. It provides a measure of the average distance of individual data points from the mean.
In this case, the dataset is relatively small, and the values are already sorted. We can calculate the IQR and MAD to compare which measure of variability best describes the spread of the dataset.
Calculating the IQR:
Q1 = 9.00
Q3 = 10.50
IQR = Q3 - Q1 = 10.50 - 9.00 = 1.50
Calculating the MAD:
Mean = (7.75 + 8.00 + 8.25 + 8.50 + 8.50 + 8.75 + 9.00 + 9.25 + 9.50 + 10.00 + 10.00 + 10.00 + 10.25 + 10.50 + 10.75) / 15 = 9.39
MAD = (|7.75 - 9.39| + |8.00 - 9.39| + |8.25 - 9.39| + |8.50 - 9.39| + |8.50 - 9.39| + |8.75 - 9.39| + |9.00 - 9.39| + |9.25 - 9.39| + |9.50 - 9.39| + |10.00 - 9.39| + |10.00 - 9.39| + |10.00 - 9.39| + |10.25 - 9.39| + |10.50 - 9.39| + |10.75 - 9.39|) / 15
= 0.71
When comparing the IQR with the MAD, we can see that the IQR is larger (1.50) than the MAD (0.71).
Therefore, the measure of variability that best describes the spread of the dataset is the IQR (1).
Answer: 1