Answer:
Q₃ - Q₂ > Q₂ - Q₁
$550,000 > $100,000
Therefore, the distribution is expected to be right skewed.
Since the distribution is right-skewed, the median would best represent a typical observation in the data.
Since the distribution is right-skewed, The inter-quartile range (IQR) would be a better choice to represent the variability of data.
Step-by-step explanation:
Housing prices in a country where 25% of the houses cost below $350,000.
Which means that first quartile is Q₁ = $350,000
50% of the houses cost below $450,000.
Which means that second quartile is Q₂ = $450,000
75% of the houses cost below $1,000,000
Which means that third quartile is Q₃ = $1,000,000
Recall that the distribution will be symmetric if the following relation holds true
Q₃ - Q₂ = Q₂ - Q₁
Q₃ - Q₂ = $1,000,000 - $450,000 = $550,000
Q₂ - Q₁ = $450,000 - $350,000 = $100,000
Hence the distribution is not symmetric since
Q₃ - Q₂ ≠ Q₂ - Q₁
The distribution is right skewed since
Q₃ - Q₂ > Q₂ - Q₁
$550,000 > $100,000
Therefore, the distribution is expected to be right skewed.
Since the distribution is right-skewed, the median would best represent a typical observation in the data
Therefore, A typical observation is best represented by the median.
Since the distribution is right-skewed, The inter-quartile range (IQR) would be a better choice to represent the variability of data.
Therefore, the variability in the observations is best measured by the inter-quartile range (IQR).
Note:
For a symmetric distribution, the mean would best represent a typical observation in the data and the variability of observations would be best represented using the standard deviation.
