Chapter 3 - QMB2100 Flashcards
What are the 2 measures studied in chapter 3?
Measure of location and measure of dispersion.
What is a measure of location?
Is a type of measure that pinpoints the center of distribution of data.
What is a measure of dispersion?
Is a type of measure that describes how the data is distributed.
What are 5 types of measures of location?
Arithmetic mean, median, mode, weighted mean, and geometric mean.
What are the 2 types of arithmetic mean?
Population mean and sample mean.
What is the equation for population mean?
μ = Σx/N ; where μ is population mean, x is any particular value within the population, and N is the number of values in the population.
What is a parameter?
Any measurable characteristic of a population.
What is the equation for the sample mean?
x̄ = Σx/n ; where x̄ is sample mean, x is any particular value within the sample, and n is the number of values in the sample.
What is a statistic?
Any measurable characteristic of a sample.
What are the 4 properties of the arithmetic mean?
- To compute a mean, the date must be measured at the interval or ratio level.
- All the values are included in computing the mean.
- The mean is unique; there is only one mean in a set of data.
- The sum of the deviations of each value from the mean is zero; Σ(x - x̄) = 0.
What is one weakness of the mean?
If one or two of these values are either extremely large or extremely small compared to the majority of data, the mean might not be an appropriate average to represent the data.
What is the formula for the mean in excel?
=AVERAGE
What is the median?
The midpoint of the values after they have been ordered from the minimum to the maximum values.
What is one advantage of the median?
The center for data containing one or two very large or very small values is better described and represented by using the median.
What levels of measurement can be used for the median?
Ordinal, interval, and ratio.
How is the median determined for an even number of observations?
By calculating the mean of the two middle observations.
What are 2 properties of the median?
- It is not affected by extremely large or small values.
- It can be computed for ordinal-level data or higher.
What is the mode?
The value of the observation that appears most frequently.
Why is the mode useful?
Useful to summarize qualitative, nominal data.
What is one advantage of the mode?
Extremely high or low values do not affect its value.
What are 2 disadvantages of the mode?
For many data sets there can be no mode or some data sets have more than one mode.
What is bimodal?
A data set with 2 modes.
What is the formula for the median on excel?
=MEDIAN
What is the formula for the mode on excel?
=MODE
What are the 3 types of distributions?
Symmetrical distribution, positively skewed distribution, and negatively skewed distribution.
Where is the relative position of the mean, median, and mode in a symmetrical distribution?
All three measures of location are at the center of the distribution.
Describe the shape and relative position of the mean, median and mode of a positively skewed distribution?
They have a long tail to the right; the mode is on the left, the median on the center and the mean towards the right.
Describe the shape and relative position of the mean, median and mode of a negatively skewed distribution?
They have a long tail to the left; the mode is on the right, the median on the center and the mean towards the left.
Why is it convenient to use the weighted mean?
Is convenient way to compute the arithmetic mean when there are several observations of the same value.
What is the equation for the weighted mean?
x̄w = Σ(wx) / Σw ; where x̄w is the weighted mean, w is the weight or frequency counts for each x value, and x is any particular value.
What is the application of the geometric mean?
To find average rates of change over time.
What is the equation for the geometric mean?
GM = n√ (x1)(x2)…(xn) ; where n is the number of values and x is any particular value.
What is one property of the geometric mean?
The geometric mean will always be less than or equal to the arithmetic mean but never greater.
What is one condition for xn values in the geometric mean?
They must always be positive.
Describe the second application for the geometric mean?
It can be used to calculate the rate of increase over time for two values.
What is the equation for the rate of increase over time?
GM = [n√ (value at end period/value at start period)] - 1 ; where n is the number of (days, months, years).
What is the formula for the geometric mean in excel?
=GEOMEAN
What is the formula for the weighted mean in excel?
=SUMPRODUCT(values, weight) / SUM(weight)
What are 2 reasons to study dispersion?
Because it describes how the data is distributed and is easy to compare the spread in two or more distributions.
What are the 3 types of measures of dispersion?
Range, variance, and standard deviation.
What is the range?
The range is the difference between the maximum and minimum values in the date set.
How is the range expressed?
As an interval.
What is one limitation of the range?
It only considers the maximum and minimum values.
What is the variance?
The arithmetic mean of the squared deviations from the mean.
What are 2 types of variance?
The population variance and the sample variance.
What is the equation for the population variance?
σ^2 = Σ(x - μ)^2 / N ; where σ^2 is the population variance, μ is the arithmetic mean of the population, N is the number of observations in the population, and x is any particular value in the population.
What is the formula for variance in excel?
=VAR.P
What is one advantage of the variance over the range?
It uses all the values in the computation.
What is the equation for sample variance?
s^2 = Σ(x - x̄)^2 / n - 1 ; where s^2 is sample variance, x̄ is the arithmetic mean of the sample, n is the number of observations in the sample, and x is any particular value within the sample.
What is the population standard deviation?
It is the square root of the population variance.
What is the equation for the population standard deviation?
σ = √[Σ(x - μ)^2 / N] ; where σ is the population standard deviation, μ is the arithmetic mean of the population, N is the number of observations in the population, and x is any particular value in the population.
What is the formula for sample variance in excel?
=VAR.S
What is the formula for population standard deviation in excel?
=STDEV.P
What is the formula for sample standard deviation in excel?
=STDEV.S
What is the equation for the sample standard deviation?
s = √[Σ(x - x̄)^2 / n - 1] ; where s is sample standard deviation, x̄ is the arithmetic mean of the sample, n is the number of observations in the sample, and x is any particular value within the sample.
What is the Chebysev’s Theorem used for?
Defines better the dispersion of data around the mean for data values with a large standard deviation that are widely scattered about the mean.
Define Chebysev’s theorem.
For any set of observations the proportion of the values that lie within k standard deviations of the mean is at least 1 - 1/k^2; where k is any value greater than 1.
Define the Empirical Rule.
For a symmetrical, bell-shaped frequency distribution, approximately 68% of the observations will lie within +/- 1 standard deviation of the mean, about 95% of the observations will lie within +/- 2 standard deviations of the mean, and 99.7% will lie within +/- 3 standard deviations of the mean.
How is the empirical rule calculated?
68% are found by x̄ +/- 1s
95% are found by x̄ +/- 2s
99.7% are found by x̄ +/- 3s;
where x̄ is the arithmetic mean and s is the standard deviation.
