Ap Statistics Chapter 3
Vocabulary for Chapter 3 – Numerically Summarizing Data
Arithemetic mean ‐ The arithmetic mean of a variable is computed by adding all the values of the variable in the data set and dividing by the number of observations.
Population arithmetic mean ‐ The population arithmetic mean, µ, is computed using all the individuals in a population and is a parameter.
Sample arithmetic mean ‐ The sample arithmetic mean, x , is computed using sample data and is a statistic. Mean – Although other types of means exist, the arithmetic mean is generally referred to as the mean.
Median ‐ The median of a variable is the value that lies in the middle of the data when arranged in ascending order.
Resistant ‐ A numerical summary of data is said to be resistant if extreme values (very large or small) …show more content…
Bimodal – If a set of data has two values of the variable that occur with the most frequency, we say the data set is bimodal.
Multimodal ‐ If a data set has three or more data values that occur with the highest frequency, the data set is multimodal.
Dispersion – Dispersion is the degree to which the data are spread out.
Range ‐ The range, R, of a variable is the difference between the largest and smallest data value.
Deviation about the Mean ‐ For a population, the deviation about the mean for the ith observation is x i – µ. For a sample, the deviation about the mean for the ith observation is xi x .
Population standard deviation ‐ The population standard deviation, σ, of a variable is the square root of the sum of squared deviations about the population mean divided by the number of observations in the population, N.
That is, it is the square root of the mean of the squared deviations about the population mean.
Sample standard deviation ‐ The sample standard deviation, s, of a variable is the square root of the sum of squared deviations about the sample mean divided by the n – 1, where n is the sample …show more content…
Degrees of freedom – For the sample standard deviation, this refers to the fact that we divide by n – 1 to compute standard deviation rather than n. We call n – 1 the degrees of freedom because the first n – 1 observations have freedom to be whatever value they wish, but the nth value has no freedom. It must be whatever value forces the sum of the deviations about the mean to equal zero.
Bias ‐ Whenever a statistic consistently underestimates a parameter, it is said to be biased.
The Empirical Rule ‐ If a distribution is roughly bell shaped, then (a) Approximately 68% of the data will lie within 1 standard deviation of the mean. (b) Approximately 95% of the data will lie within 2 standard deviations of the mean. (c) Approximately 99.7% of the data will lie within 3 standard deviations of the mean. Weighted mean ‐ The weighted mean, x w , of a variable is found by multiplying each value of the variable by its corresponding weight, adding these products, and dividing this sum by the sum of the weights. z‐score ‐ The z‐score represents the distance that a data value is from the mean in terms of the
Arithemetic mean ‐ The arithmetic mean of a variable is computed by adding all the values of the variable in the data set and dividing by the number of observations.
Population arithmetic mean ‐ The population arithmetic mean, µ, is computed using all the individuals in a population and is a parameter.
Sample arithmetic mean ‐ The sample arithmetic mean, x , is computed using sample data and is a statistic. Mean – Although other types of means exist, the arithmetic mean is generally referred to as the mean.
Median ‐ The median of a variable is the value that lies in the middle of the data when arranged in ascending order.
Resistant ‐ A numerical summary of data is said to be resistant if extreme values (very large or small) …show more content…
Bimodal – If a set of data has two values of the variable that occur with the most frequency, we say the data set is bimodal.
Multimodal ‐ If a data set has three or more data values that occur with the highest frequency, the data set is multimodal.
Dispersion – Dispersion is the degree to which the data are spread out.
Range ‐ The range, R, of a variable is the difference between the largest and smallest data value.
Deviation about the Mean ‐ For a population, the deviation about the mean for the ith observation is x i – µ. For a sample, the deviation about the mean for the ith observation is xi x .
Population standard deviation ‐ The population standard deviation, σ, of a variable is the square root of the sum of squared deviations about the population mean divided by the number of observations in the population, N.
That is, it is the square root of the mean of the squared deviations about the population mean.
Sample standard deviation ‐ The sample standard deviation, s, of a variable is the square root of the sum of squared deviations about the sample mean divided by the n – 1, where n is the sample …show more content…
Degrees of freedom – For the sample standard deviation, this refers to the fact that we divide by n – 1 to compute standard deviation rather than n. We call n – 1 the degrees of freedom because the first n – 1 observations have freedom to be whatever value they wish, but the nth value has no freedom. It must be whatever value forces the sum of the deviations about the mean to equal zero.
Bias ‐ Whenever a statistic consistently underestimates a parameter, it is said to be biased.
The Empirical Rule ‐ If a distribution is roughly bell shaped, then (a) Approximately 68% of the data will lie within 1 standard deviation of the mean. (b) Approximately 95% of the data will lie within 2 standard deviations of the mean. (c) Approximately 99.7% of the data will lie within 3 standard deviations of the mean. Weighted mean ‐ The weighted mean, x w , of a variable is found by multiplying each value of the variable by its corresponding weight, adding these products, and dividing this sum by the sum of the weights. z‐score ‐ The z‐score represents the distance that a data value is from the mean in terms of the