Maria surveyed girls on the amount (in $) they spent on a dress for the middle school spring fling:
79, 79, 79, 82, 84, 85, 89, 90, 99, 100, 100, 100, 129, 139, 155, 174, 189, 200, 209, 250
Which measure of variability—IQR or MAD—best describes the spread of the dataset?
(1 point)
Responses
IQR; the data distribution is skewed
IQR; the data distribution is skewed
MAD; the data distribution has outliers
MAD; the data distribution has outliers
MAD; the data distribution is symmetrical
MAD; the data distribution is symmetrical
IQR; the data distribution is symmetrical
Well, it seems like these girls spent quite a range of money on their dresses for the spring fling! Now, to answer your question, I would say that the measure of variability that best describes the spread of the dataset is the IQR. Why, you ask? Because the data distribution is skewed. It's like those girls with their dresses, making the data lean more towards one side.
The correct response is:
IQR; the data distribution is skewed
To determine whether the IQR (Interquartile Range) or MAD (Mean Absolute Deviation) best describes the spread of the dataset, we need to consider the characteristics of the data distribution.
First, let's compute the IQR. The IQR represents the range between the first quartile (Q1) and the third quartile (Q3). To find it, we need to arrange the data in ascending order:
79, 79, 79, 82, 84, 85, 89, 90, 99, 100, 100, 100, 129, 139, 155, 174, 189, 200, 209, 250
Next, we find the position of the first quartile (Q1) and the third quartile (Q3):
Q1 = 87.5
Q3 = 191.5
Now, we can calculate the IQR:
IQR = Q3 - Q1 = 191.5 - 87.5 = 104
Now, let's consider the MAD. The MAD measures the average distance between each data point and the mean.
To compute the MAD, we need to calculate the mean (average) of the dataset:
Mean = (79 + 79 + 79 + 82 + 84 + 85 + 89 + 90 + 99 + 100 + 100 + 100 + 129 + 139 + 155 + 174 + 189 + 200 + 209 + 250) / 20 = 128.6 (approximately)
Next, we find the absolute deviations of each data point from the mean:
|79 - 128.6| = 49.6
|79 - 128.6| = 49.6
|79 - 128.6| = 49.6
|82 - 128.6| = 46.6
|84 - 128.6| = 44.6
|85 - 128.6| = 43.6
|89 - 128.6| = 39.6
|90 - 128.6| = 38.6
|99 - 128.6| = 29.6
|100 - 128.6| = 28.6
|100 - 128.6| = 28.6
|100 - 128.6| = 28.6
|129 - 128.6| = 0.4
|139 - 128.6| = 10.4
|155 - 128.6| = 26.4
|174 - 128.6| = 45.4
|189 - 128.6| = 60.4
|200 - 128.6| = 71.4
|209 - 128.6| = 80.4
|250 - 128.6| = 121.4
Now we calculate the MAD:
MAD = (49.6 + 49.6 + 49.6 + 46.6 + 44.6 + 43.6 + 39.6 + 38.6 + 29.6 + 28.6 + 28.6 + 28.6 + 0.4 + 10.4 + 26.4 + 45.4 + 60.4 + 71.4 + 80.4 + 121.4) / 20 ≈ 48.68 (approximately)
Now, based on the computation, we can compare the IQR and MAD to determine which measure of variability best describes the spread of the dataset.
Since the IQR is 104 and the MAD is approximately 48.68, we can observe that the IQR is approximately twice as large as the MAD, indicating a larger spread. This suggests that there may be outliers in the dataset.
Therefore, the correct answer is:
MAD; the data distribution has outliers