Studied by 14 peopleWhat is a Density Curve? Can it determine a specific value?
It models the distribution of a continuous quantitative variable with a curve that is always on or above the horizonal axis and has an area of exactly 1 beneath it. It is an approximation, density curve cannot determine a specific value.
What graphs can you use to plot Quantitative Data? What do you look for in these graphs?
Dotplot, Histogram, Stemplot.
Shape, Center, Spread, outliers.
What does proportion mean?
It is the area under the density curve and above any interval of values on the horizonal axis. It estimates all observations that fall in that interval.
Describe “True Populations” and “Estimated Samples”. Give their measurements, standard deviation and mean.
Measurements - Parameter (true), Statistic (estimated)
Standard Deviation - Mu (true), x bar (estimated)
Mean - sigma/o (true), Sx (estimated)
Describe the Mean and Median in a density curve…
Mean - The point at which the curve would balance if made of solid material
Median - The point that divides the area under the curve in half.
A skewed right distribution has a higher __
mean
Define a normal distribution
A symmetric, single-peaked, bell-shaped density curve (normal curve) that has two parameters: mean and standard deviation.
All normal curves….
Have shape, are symmetric, single-peak, and bell-shaped.
Are described by its mean and standard deviation
Mean=Median, both are at the center.
If the mean changes, the curve shifts left of right.
Standard Deviation controls spread.
Give the percentages from left to right of a 68-95-99.7 rule
0.15%, 2.35%, 13.5%, 34%, 34%, 13.5%, 2.35%, 0.15%. Each are in one standard deviation of one another.
The 68-95-99.7 rule describes distributions that are ____ normal.
exactly
What is the Standard Normal Distribution? What is the z-score formula?
A mean of 0 and a standard deviation of 1. YOU NEED TO SAY THIS IN Z-SCORES; NOT REGULAR UNITS.
equation: z= (x-u)/o [sx]
EXAMPLE PROBLEM: Martin keeps track of his daily calorie intake which is approximately normal with a mean of 2730 calories and a standard deviation of 530 calories. One day, he had ate a total of 3900 calories. How often is this to occur?
Use z-score formula: z= (x-u)/o
Z-score is 2.21. Use Z-score table to find out this.
Answer: 1.4%
What does Inverse Normal Find?
The range of data given a proportion (EX: 30% of the data shows ____)
What is a normal probability plot?
A scatterplot of (data value, expected z-score) for each of the individuals in a quantitative data set. The x-coordinate is the actual data value and the y-coordinate is the expected z-score.
Empirical Rule Steps are….
Calculate the Mean and Standard Deviation
Count numbers of observations between 1, 2, and 3 standard deviations from the mean.
Check the 68-95-99.7 rule.
How do you interoperate a percentile?
CONTEXT is greater than or equal to ___ % of context
EX:
Mr. Withe’s temperature is greater than or equal to 20% of 131 people studied.
What is a cumulative relative frequency graph?
It plots a point corresponding to the percentile of a given value in a distribution of quantitative data.
EX: 86 wins equates to 67 percentile.
What does adding a constant do to a data set?
Moves the center, does not change variability or spread (range, IQR, standard deviation). THIS MEANS YOU DO NOT ADD A CONSTANT TO A STANDARD DEVIATION!!!!
What does multiplying a constant do?
Changes spread and center, not the shape.
Nearly everything is multiplied (sx, o, u, IQR)
Note
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