Miniature golf scores for a group of friends follows:
30, 32, 36, 40, 44, 45, 46, 48, 55, 58, 59, 60, 76, 82, 90
Which measure of variability—IQR or MAD—best describes the spread of the dataset? Enter 1 for IQR or 2 for MAD.
(1 point)
1
To determine which measure of variability, IQR or MAD, best describes the spread of the dataset, we need to calculate both values and compare them.
1. IQR (Interquartile Range):
To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3).
Q1 = (n+1)/4 = (15+1)/4 = 4th value = 40
Q3 = 3*(n+1)/4 = 3*(15+1)/4 = 12th value = 60
IQR = Q3 - Q1 = 60 - 40 = 20
2. MAD (Mean Absolute Deviation):
To calculate the MAD, we need to find the mean (M) and the absolute deviation (AD) for each data point.
M = (30 + 32 + 36 + 40 + 44 + 45 + 46 + 48 + 55 + 58 + 59 + 60 + 76 + 82 + 90) / 15 = 748 / 15 ≈ 49.87
AD = |data point - M|
AD = |30-49.87| + |32-49.87| + ... + |82-49.87| + |90-49.87|
AD = 19.87 + 17.87 + ... + 32.13 + 40.13
AD ≈ 274.6
Comparing the IQR (20) and MAD (274.6) values, we can conclude that the MAD value is significantly larger than the IQR. This suggests that MAD would be the better measure of variability to describe the spread of the dataset.
Therefore, the answer is 2 for MAD.