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