Quantitative Skills Workshop Flashcards
Manipulating Exponents: x^-a –> ?
1/x^a
Manipulating exponents: x^a*x^b —> ?
x^(a+b)
Manipulating logarithms:
log(1) = ?
0
Manipulating logarithms:
log(x*y) = ?
log x + log y
Manipulating logarithms:
log(x/y) = ?
log x - log y
Manipulating logarithms:
log(x^y) = ?
y log x
Calculus concepts:
To find the derivative on a graph, what should you look at?
The slope of the line or the slope of a curve at a certain region
Calculus concepts: To find the integral of a graph, what should you look at?
The area under the curve
To find inflection points given an equation, what should you do?
Take the second derivative and set it equal to zero.
How can you determine whether the location of your inflection point is a local maximum (apex) or minimum?
Check for concavity at the left and right of your inflection point. For a maximum you should go from a positive to negative slope and for a minimum you should go from a negative to a positive slope. at the inflection point.
What are the 4 data types?
Sample vs population data and quantitative vs qualitative data
What are some statistical tools to measure centers of data?
Mean, median and mode
How can you measure variance?
By looking at the range or variance
List 4 types of normal distributions.
Mean, standard deviation, standard error and confidence intervals.
What are 3 types of hypothesis testing?
Null-hypothesis, p-value, statistical significance
What is single variable regression?
?
What are the two types of qualitative or categorical data?
Nominal and ordinal
Define nominal data.
Has a label with no numerical value or order
Define ordinal data.
Labels can be ordered or ranked, but do not have exact numerical meaning
What are two types of quantitative data?
Interval and ratio
Define interval data.
Contains numerical values such that the interval (space between numbers) is precisely defined
Define ratio data.
Contains numerical values such that the interval is precisely defined and the number zero has meaning
Define mean, median, and mode.
Mean: the average of all measured values
Median: the middle measurement of a data set when arranged in numerical order
Mode: the most frequently occurring value
What is the purpose of a confidence interval?
To make a statement that we are confident that the population mean is somewhere within an interval around the sample mean
The standard deviation plus what range of values covers the margin of error?
The standard deviation +/- the critical value [(Z)^(-a/2)] times the standard error [s/sqrt(n)] is the margin of error, as shown in the image on slide 16 of the Quantitative Skills Workshops.
Describe null hypothesis.
The null hypothesis is denoted by Ho and is assumed to be true unless proven otherwise.
Given a sample size n, a mean of x and a sample standard deviation of s, what is the overall standard deviation?
s/sqrt(n), where s is the sample standard deviation and n is the sample size.
What does the p value describe?
The probability that the sample comes from a population where the null hypothesis is true.
Describe the linear correlation coefficient.
The linear correlation coefficient is denoted by r and is tells us how close the relationship (graph trend) is to a line. The closer to 1, the more linear it is.
What is the coefficient of determination?
The coefficient of determination is r^2, and it tells us variability in the data from the best fit line. The closer r^2 is to 1, the better the fit.
