HBX Business Analytics: Questions With Complete
Solutions
Skewness Right Ans - Skewness measures the degree of a graph's
asymmetry. If the right tail is longer, we say the distribution is skewed to the
right or "right-tailed." Likewise, if the left tail is longer, we say the distribution
is skewed to the left or "left-tailed."
Rules of thumb for the normal distribution Right Ans - About 68% of the
probability is contained in the range reaching one standard deviation away
from the mean on either side:
P(μ−σ≤x≤μ+σ)≈68%
About 95% of the probability is contained in the range reaching two standard
deviations (1.96 to be exact) away from the mean on either side:
P(μ−2σ≤x≤μ+2σ)≈95%
We'll use two standard deviations when discussing the normal distribution
conceptually, but we will always use 1.96 for actual calculations in Excel.
About 99.7% of the probability is contained in the range reaching three
standard deviations away from the mean on either side:
P(μ−3σ≤x≤μ+3σ)≈99.7%
Bias Right Ans - avoid biased results by
- phrasing questions neutrally
, -ensuring that the sampling method is appropriate for the demographic of the
target population
-pursuing a high response rate
Normal Distribution Right Ans - a unique symmetrical shape whose centre
and width are determined by its mean and standard deviation respectively.
z-value Right Ans - the distance that x lies from the mean, measured in
standard deviations.
Central Limit Theorem Right Ans - If we take enough sufficiently large
samples from any population, the means of those samples will be normally
distributed regardless of the shape of the underlying population.
Confidence interval Right Ans - An estimate of the range in which the true
population mean likely lies.
Outlier Right Ans - Technically, a data point is considered an outlier if it is
more than a specified distance below the lower quartile or above the upper
quartile of a data set. Let's start with a couple of definitions. The lower
quartile, Q1, is the 25th percentile—by definition, 25% of all observations fall
below Q1. The upper quartile, Q3, is the 75th percentile—75% of all
observations fall below Q3. The interquartile range (IQR) is the difference
between the upper and lower quartiles, that is, IQR=Q3-Q1.
Histogram Right Ans - Histogram, also called a bar chart.
Solutions
Skewness Right Ans - Skewness measures the degree of a graph's
asymmetry. If the right tail is longer, we say the distribution is skewed to the
right or "right-tailed." Likewise, if the left tail is longer, we say the distribution
is skewed to the left or "left-tailed."
Rules of thumb for the normal distribution Right Ans - About 68% of the
probability is contained in the range reaching one standard deviation away
from the mean on either side:
P(μ−σ≤x≤μ+σ)≈68%
About 95% of the probability is contained in the range reaching two standard
deviations (1.96 to be exact) away from the mean on either side:
P(μ−2σ≤x≤μ+2σ)≈95%
We'll use two standard deviations when discussing the normal distribution
conceptually, but we will always use 1.96 for actual calculations in Excel.
About 99.7% of the probability is contained in the range reaching three
standard deviations away from the mean on either side:
P(μ−3σ≤x≤μ+3σ)≈99.7%
Bias Right Ans - avoid biased results by
- phrasing questions neutrally
, -ensuring that the sampling method is appropriate for the demographic of the
target population
-pursuing a high response rate
Normal Distribution Right Ans - a unique symmetrical shape whose centre
and width are determined by its mean and standard deviation respectively.
z-value Right Ans - the distance that x lies from the mean, measured in
standard deviations.
Central Limit Theorem Right Ans - If we take enough sufficiently large
samples from any population, the means of those samples will be normally
distributed regardless of the shape of the underlying population.
Confidence interval Right Ans - An estimate of the range in which the true
population mean likely lies.
Outlier Right Ans - Technically, a data point is considered an outlier if it is
more than a specified distance below the lower quartile or above the upper
quartile of a data set. Let's start with a couple of definitions. The lower
quartile, Q1, is the 25th percentile—by definition, 25% of all observations fall
below Q1. The upper quartile, Q3, is the 75th percentile—75% of all
observations fall below Q3. The interquartile range (IQR) is the difference
between the upper and lower quartiles, that is, IQR=Q3-Q1.
Histogram Right Ans - Histogram, also called a bar chart.
