Stats and Probability Ch3
Chebyshev's theorem
The proportion of values from a data set that will fall within k standard deviations of the mean will be at least , where k is a number greater than 1 (k is not necessarily an integer).
range
The range is the highest value minus the lowest value. The symbol R is used for the range.
sample mean
The sample mean, denoted by (pronounced "X bar"), is calculated by using sample data. The sample mean is a statistic. where n represents the total number of values in the
mode
The value that occurs most often in a data set is called the mode.
symmetric distribution
the data values are evenly distributed on both sides of the mean.
multimodal
If a data set has more than two values that occur with the same greatest frequency, each value is used as the mode, and the data set is said to be multimodal.
bimodal
If a data set has two values that occur with the same greatest frequency, both values are considered to be the mode and the data set is said to be bimodal.
positively skewed
In a positively skewed or right-skewed distribution, the majority of the data values fall to the left of the mean and cluster at the lower end of the distribution
unimodal
data set that has only one value that occurs with the greatest frequency is said to be unimodal.
Percentiles
divide the data set into 100 equal groups.
population variance
is the average of the squares of the distance each value is from the mean. The symbol for the population variance is ( is the Greek lowercase letter sigma).
mean
is the sum of the values, divided by the total number of values.
weighted mean
-The type of mean that considers an additional factor is called the weighted mean, and it is used when the values are not all equally represented. -Find the weighted mean of a variable X by multiplying each value by its corresponding weight and dividing the sum of the products by the sum of the weights.
standard score
A z score or standard score for a value is obtained by subtracting the mean from the value and dividing the result by the standard deviation. The symbol for a standard score is zThe z score represents the number of standard deviations that a data value falls above or below the mean.
coefficient of variation
The coefficient of variation, denoted by CVar, is the standard deviation divided by the mean. The result is expressed as a percentage.
median
The median is the midpoint of the data array. The symbol for the median is MD.
midrange
The midrange is defined as the sum of the lowest and highest values in the data set, divided by 2. The symbol MR is used for the midrange.
population mean
The population mean, denoted by (pronounced "mew"), is calculated by using all the values in the population. The population mean is a parameter. where N represents the total number of values in the population.
population standard deviation
The population standard deviation is the square root of the variance. (nshould be capitol in image)
no mode
When no data value occurs more than once, the data set is said to have no mode. Note: Do not say that the mode is zero.
negatively skewed
When the majority of the data values fall to the right of the mean and cluster at the upper end of the distribution, with the tail to the left, the distribution is said to be negatively skewed or left-skewed.
parameter
a characteristic or measure obtained by using all the data values from a specific population.
statistic
a characteristic or measure obtained by using the data values from a sample.
