Economics and Stats Exam 1
The median for the data set: 10, 6, 4, 9, 5 is
6
Emperical Rule
68% of all data is within one standard deviations of the mean 95% of all data is within two standard deviations of the mean 99.7% of all data is within three standard deviations of the mean (describes what is expected)
left skewed
A density curve where the left side of the distribution extends in a long tail. (Mean < median.)
Which of the following can be used to determine the proportion of data points that fall within a specified number of standard deviations from the mean? -The mode -Empirical rule -Chebyshev's therom -Percentiles
Empirical rule -Chebyshev's theorem
How to show variation in data values?
Histograms and dot plots
median
It separates the upper and lower half . It is the middle observation in a odd set or it is the average of the middle two values divided by 2. Ex 15+17/2. It is not always a clean split if a value repeats.
Which of the following are measures of center of a data set? Multiple select question. -Mean -Variance -Standard deviation -Mode -Median
Mean, median ,mode
The square root of the average squared deviation of data values from their mean is known as the...
Standard Deviation
Numbers that summarize a sample of data are called_____and numbers that summarize populations are called______
Statistics and parameters
Mode
The value that occurs most frequently in a given data set. Only useful for Categorical data, doesn't help with continuous (data values don't repeat). It is good for a small range.
The arithmetic mean is the average of a data set.
True
Which of the following statements is true? Multiple select question. -If two data sets have the same mean they must have the same standard deviation. -Two data sets could have the same mean but different standard deviations. -Two data sets could have different means but the same standard deviation. -If two data sets have different means they must have different standard deviations.
Two data sets could have the same mean but different standard deviations. -Two data sets could have different means but the same standard deviation.
right skewed
a distribution with a tail that extends to the right. Mean > median
When comparing two data sets with different units of measurement, what is the relative measure of dispersion?
coefficient of the variation
A unit-free measure of dispersion is
coefficient of variation.
True or false: The standard deviation can be a negative value.
false
symmetric data...
mean and median are about the same
When monitoring a process distribution, both the ______ and the ____ must be tracked
mean and the variation
The best measure of central location for a numerical data set when the data set contains outliers is the
median
The first step to determine the median is to
place the data in numerical order
Shape
shows us if the data is skewed or symmetric. Shows if its flat, peaked, or bimodal.
Variability
shows variability, dispersion of data, and how spread out the data values are.
A measure used to gauge the position of items within a data array is
standard deviation
sample variance
s²
mean
the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores. It counterbalances with the data values above and below it. (it is the center)
mean absolute deviation
the average distance between each data value and the mean (center).
range
the difference between the highest and lowest scores in a distribution (Xmax- Xmin)
Midrange
the value midway between the maximum and minimum values in the original data set
The average squared difference of data values from their mean is the
variance
center
where the data values are concentrated, in the middle of the data values.
The sum of deviation from mean is always
zero
population variance
σ²
Standard deviations can be compared Multiple select question. -for data sets with different measurement units. -for data sets with the same measurement units. -for data sets with the same measurement units but greatly different magnitudes. -for data sets with the same measurement units and similar magnitude (size).
-for data sets with the same measurement units -for data sets with the same measurement units and similar magnitude
Chebyshev's Theorem
1-1/k^2 A theorem that can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean. applies to all samples