Stats Chapter 3

Point Estimator (pg.108)

A sample statistic is referred to as the point estimator of the corresponding population parameter.

Quartiles (pg.118)

Quartiles are specific percentiles. First Quartile= Q1= 25th Percentile Second Quartile= Q2= 50th Percentile Third Quartile= Q3= 75th Percentile

Percentile (pg.117)

A percentile provides information about how the data are spread over the interval from the smallest value to the largest value. *We must arrange the data in ascending order (smallest value to largest value)* ~ The smallest value is in position 1, the next smallest value is in position 2, and so on. *Equation*

Skewness (pg.135)

An important (numerical) measure of the shape of a distribution. - Can be easily computed using statistical software. Figure 3.9 (pg.136) *Equation*<--- not important though

Trimmed Mean (pg.111)

Another measure, sometimes used when extreme values are present. -It is obtained by deleting a percentage of the smallest and largest values from a data set and then computing the mean of the remaining values. Ex. The 5% trimmed mean is obtained by removing the smallest 5% and the largest 5% of the data values and then computing the mean of the remaining values.

Z-Score (pg.136)

Can be interpreted as the number of standard deviations x is from the mean ____. i x -Is often called the standardized value. -An observation's z-score is a measure of the relative location of the observation in a data set. -A data value less than the sample mean will have a z-score less than zero. - A data value greater than the sample mean will have a z-score greater than zero. -A data value equal to the sample mean will have a z-score of zero. *Equation*

Five-Number Summary (pg.143)

Five numbers are used to summarize the data. 1.) Smallest Value (MIN) 2.) First Quartile (Q1) 3.) Median (Q2) 4.) Third Quartile (Q3) 5.) Largest Value (MAX) Summary statistics and easy-to-draw graphs can be used to quickly summarize large quantities of data.

Population Parameters (pg.108)

If the measures are computed for data from a population. *Equation*

Sample Statistics (pg.108)

If the measures are computed for data from a sample. *Equation*

Coefficient of Variation (pg.130)

Indicates how large the standard deviation is in the relation to the mean. *Equation*

Box Plot (pg.143)

Is a graphical summary of data that is based on a five-number summary. - A key to the development of a box plot is the computation of the median (interquartile range) and the quartiles Q1 and Q3. IQR= Q3-Q1 Summary statistics and easy-to-draw graphs can be used to quickly summarize large quantities of data. ~Box plots provide another way to identify outliers. *Equation* not really but look at notes!

Outliers (pg.139)

Is an unusually small or unusually large value in a data set. -A data value with a z-score less than -3 or greater than +3 might be considered an outlier.

Median (pg.110)

Is the value in the middle when the data items are arranged in ascending order. -Whenever a data set has extreme values, the median is the preferred measure of central location. ~ The median is the measure of location most often reported for annual income and property value data. ~ A few extremely large incomes or property values can inflate the mean. Arrange the data in ascending order (smallest to largest): a.) For an ODD # of observations, the median is the middle value. b.) for an EVEN # of observations, the median is the average of the two middle values.

Mode (pg.111)

Is the value that occurs with greatest frequency. -The greatest frequency can occur at two or more different values. -Biomodal: If the data have exactly two modes (pg.112) -Multimodal: If the data have more than two modes (pg.112) ***In multimodal cases the mode is almost never reported bc listing three or more modes would not be particularly helpful in describing a location for the data.***

Mean (pg.108)

Perhaps the most important measure of location is the mean, or average value, for a variable. -The means provides a measure of central location for the data. -The mean of the data set is the average of all the data values. -The sample mean is the pointer estimator of the population mean. SAMPLE Mean Formula (pg.108) POPULATION Mean Formula (pg.110)

Drilling Down

Refers to functionality in interactive dashboards that allows the user to access information and analyses at increasingly detailed level.

Interquartile Range (IQR) (p.126)

The interquartile range of a data set is the difference between the third quartile and the first quartile. -It is the range for the middle 50% of the data. -It overcomes the sensitivity to extreme data values. *Equation*

Weighted Mean (pg.113)

The mean is computed by giving each observation a weight that reflects its relative importance. *Equation*

Range (pg.125)

The range of a data set is the difference between the largest and smallest data values. Range= Largest Value- Smallest Value -It is the simplest measure of variability. -It is very sensitive to the smallest and largest data values. ~ It is seldom used as the only measure bc its based on only two of the observations and thus is highly influenced by extreme values. *Equation*

Standard Deviation (pg.128)

The standard deviation of a data set is the positive square root of the variance. -Is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. -It is measured in the same units as the data, making it more easily interpreted than the variance. -Bell Shaped Curve= Small Standard Deviation -Spread Apart and Bell Curve is Relatively Flat= Large Standard Deviation Variance= (Standard Deviation)^2 *Equation*

Variance (pg.126)

The variance is the average of the squared differences between each data value and the mean. -Is a measure of variability that utilizes all the data. -It is based on the difference between the value of each observation (xi) and the mean (𝑥 ̅ for a sample, m for a population). -The variance is useful in comparing the variability of two or more variables. Variance= (Standard Deviation)^2 *Equation*

Empirical Rule (pg.139)

When the data are believed to approximate a bell-shaped distribution ... Can be used to determine the percentage of data values that must be within a specified number of standard deviations of the mean. Figure 3.11