Cfa Level 1 Exam-Quantitative Methods
Questions And Answers With Verified
Solutions 100% Correct Rated A+ Newly
Updated 2025
Measures of central tendency - ANSWER✔✔Identify the center, or average, of a
data set and can represent typical or expected value in a data set
Ex:arithmetic mean, geometric mean, weighted mean, median, and mode.
Measures of Dispersion - ANSWER✔✔Ex:Range, mean absolute deviation, and
variance
Population Mean (arithmetic) - ANSWER✔✔all observed values in the population
are summed and divided by the number of observations in the population (N). It
can be shown by "Mew"
Sample Mean (arithmetic) - ANSWER✔✔Sum of all the values in a sample of a
population divided by the number of observations in the sample (n). Inferences
about the population and denoted by "X-Bar"
arithmetic mean - ANSWER✔✔-all interval and ratio data sets have arithmetic
mean
-all data values are included in the computation
-a data set has only one arithmetic mean
-The sum of the deviations of each obs. in the data set is zero (only central
tendency where this is possible)
-Best estimator of next years returns given only the three years of outcomes.
,Weighted mean - ANSWER✔✔recognizes that different obs. may have a
disproportionate influence on the mean
Median - ANSWER✔✔midpoint of a data set when the data is arranged in
ascending or descending order. Half above, half below. Not affected by outliers
Mode - ANSWER✔✔Value that occurs most frequently in a data set. More than
one more or even no mode
Unimodal: one value most frequently
bimodal: 2 values most frequently
trimodal: 3 values most frequently
Geometric mean - ANSWER✔✔Used when calculating investment returns over
multiple periods or when measuring compound growth rates. The geometric mean
is always less than or equal to the arithmetic mean, and the difference increases as
the dispersion increases. The only time the arithmetic and geometric means are
equal is when there is no variability in the observations. Appropriate measure of
past performance. Average annual compound return. Geometric of 8.63% tell us
the single rate that if compounded over the three periods, would lead to the same
increase in wealth as the individual annual rates of return. Good for multi-year
returns.
Harmonic mean - ANSWER✔✔Used for certain computations such as the average
cost of shares purchased over time. For values that are not equal: harmonic
mean<geometric mean<arithmetic mean
Quantile - ANSWER✔✔Value at or below which a stated proportion of the data in
a distribution lies
Distribution is divided into:
,quartile: quarters
quintile: fifths
decile: tenths
percentile: hundreths
"3rd quartile is the 75th percentile"
Ly = (n+1) x y/100
Dispersion - ANSWER✔✔Variability around the central tendency measuring risk
Range - ANSWER✔✔Distance between the largest and smallest values of a data
set Max minus Min
Mean Absolute Deviation - ANSWER✔✔Average of the absolute values of the
deviations of individual observations from the arithmetic mean. Answer is on
average +or-MAD from the mean.`
Population Variance - ANSWER✔✔The average of the squared deviations from
the mean. "The average variation from the mean return is 35.60% squared"
Population Standard Deviation - ANSWER✔✔Square root of the population
variance. STDEV will be greater than MAD
Sample Variance - ANSWER✔✔Measure of dispersion that applies when
evaluation a sample "n" observations from a population. Denominator is n-1. "X-
Bar" instead of "Mew" for the mean.
, Biased Estimator of the population variance: Sample Variance -
ANSWER✔✔Dividing just by n will underestimate the population parameter for
sample sizes. "s-squared" is an unbiased estimator of "mew-squared"
Sample Standard Deviation - ANSWER✔✔Taking the square root of the sample
variance. Unbiased estimator of the population standard deviation
Chebyshev's Inequality - ANSWER✔✔For any set of observations, whether
sample or population data and regardless of the shape of the distribution, the
percentage of the observations that lie within k standard deviations of the mean is
at least 1-1/k-squared for all k>1. Applies to any distribution
Relative Dispersion - ANSWER✔✔Amount of variability in a distribution relative
to a reference point or benchmark
Coefficient of Variation - ANSWER✔✔Standard Deviation of X/Avg Value of X.
Measures the amount of dispersion in a distribution relative to the distributions
mean. Helps with direct comparison of dispersions across data. Risk per unit of
expected return.
Variation per unit of return
Sharpe Ratio - ANSWER✔✔"Reward-to-variability" ratio that measures excess
return per unit of risk. Portfolio return minus risk free rate divided by standard
deviation of portfolio returns
Limitations: if two portfolios have negative sharpe ratios, its not true that the
higher implies superior performance. Useful only when STDEV is appropriate
measure of risk
Questions And Answers With Verified
Solutions 100% Correct Rated A+ Newly
Updated 2025
Measures of central tendency - ANSWER✔✔Identify the center, or average, of a
data set and can represent typical or expected value in a data set
Ex:arithmetic mean, geometric mean, weighted mean, median, and mode.
Measures of Dispersion - ANSWER✔✔Ex:Range, mean absolute deviation, and
variance
Population Mean (arithmetic) - ANSWER✔✔all observed values in the population
are summed and divided by the number of observations in the population (N). It
can be shown by "Mew"
Sample Mean (arithmetic) - ANSWER✔✔Sum of all the values in a sample of a
population divided by the number of observations in the sample (n). Inferences
about the population and denoted by "X-Bar"
arithmetic mean - ANSWER✔✔-all interval and ratio data sets have arithmetic
mean
-all data values are included in the computation
-a data set has only one arithmetic mean
-The sum of the deviations of each obs. in the data set is zero (only central
tendency where this is possible)
-Best estimator of next years returns given only the three years of outcomes.
,Weighted mean - ANSWER✔✔recognizes that different obs. may have a
disproportionate influence on the mean
Median - ANSWER✔✔midpoint of a data set when the data is arranged in
ascending or descending order. Half above, half below. Not affected by outliers
Mode - ANSWER✔✔Value that occurs most frequently in a data set. More than
one more or even no mode
Unimodal: one value most frequently
bimodal: 2 values most frequently
trimodal: 3 values most frequently
Geometric mean - ANSWER✔✔Used when calculating investment returns over
multiple periods or when measuring compound growth rates. The geometric mean
is always less than or equal to the arithmetic mean, and the difference increases as
the dispersion increases. The only time the arithmetic and geometric means are
equal is when there is no variability in the observations. Appropriate measure of
past performance. Average annual compound return. Geometric of 8.63% tell us
the single rate that if compounded over the three periods, would lead to the same
increase in wealth as the individual annual rates of return. Good for multi-year
returns.
Harmonic mean - ANSWER✔✔Used for certain computations such as the average
cost of shares purchased over time. For values that are not equal: harmonic
mean<geometric mean<arithmetic mean
Quantile - ANSWER✔✔Value at or below which a stated proportion of the data in
a distribution lies
Distribution is divided into:
,quartile: quarters
quintile: fifths
decile: tenths
percentile: hundreths
"3rd quartile is the 75th percentile"
Ly = (n+1) x y/100
Dispersion - ANSWER✔✔Variability around the central tendency measuring risk
Range - ANSWER✔✔Distance between the largest and smallest values of a data
set Max minus Min
Mean Absolute Deviation - ANSWER✔✔Average of the absolute values of the
deviations of individual observations from the arithmetic mean. Answer is on
average +or-MAD from the mean.`
Population Variance - ANSWER✔✔The average of the squared deviations from
the mean. "The average variation from the mean return is 35.60% squared"
Population Standard Deviation - ANSWER✔✔Square root of the population
variance. STDEV will be greater than MAD
Sample Variance - ANSWER✔✔Measure of dispersion that applies when
evaluation a sample "n" observations from a population. Denominator is n-1. "X-
Bar" instead of "Mew" for the mean.
, Biased Estimator of the population variance: Sample Variance -
ANSWER✔✔Dividing just by n will underestimate the population parameter for
sample sizes. "s-squared" is an unbiased estimator of "mew-squared"
Sample Standard Deviation - ANSWER✔✔Taking the square root of the sample
variance. Unbiased estimator of the population standard deviation
Chebyshev's Inequality - ANSWER✔✔For any set of observations, whether
sample or population data and regardless of the shape of the distribution, the
percentage of the observations that lie within k standard deviations of the mean is
at least 1-1/k-squared for all k>1. Applies to any distribution
Relative Dispersion - ANSWER✔✔Amount of variability in a distribution relative
to a reference point or benchmark
Coefficient of Variation - ANSWER✔✔Standard Deviation of X/Avg Value of X.
Measures the amount of dispersion in a distribution relative to the distributions
mean. Helps with direct comparison of dispersions across data. Risk per unit of
expected return.
Variation per unit of return
Sharpe Ratio - ANSWER✔✔"Reward-to-variability" ratio that measures excess
return per unit of risk. Portfolio return minus risk free rate divided by standard
deviation of portfolio returns
Limitations: if two portfolios have negative sharpe ratios, its not true that the
higher implies superior performance. Useful only when STDEV is appropriate
measure of risk
