Quiz #2

• The pth percentile is a number where p% of the measurements fall below that number and (100-p)% fall above it.
• The lower quartile (Q_L) is the 25th percentile of a data set.
• The middle quartile (M) is the median or 50th percentile of a data set.
• The upper quartile (Q_U) is the 75th percentile of a data set.
• This is the formula for the sample z-score.

  
• This is the formula for the population z-score.

  
• The z-score is the distance between a given measurement x and the mean of the data set. It is expressed in standard deviations.
• Concerning mount-shaped distributions of data, approx. 68% of the measurements will have a z-score between -1 and 1.
• Concerning mound-shaped distributions of data, approx. 95% of the measurements will have a z-score between -2 and 2.
• Concerning mound-shaped distributions of data, approx. 99.7% of the measurements will have a z-score between -3 and 3.
• An outlier is an observation that is unusually large or small relative to the other values in a data set.
• Outliers are attributed to one of the following cases:

  • The measurement is observed, recorded, or entered into the computer incorrectly
  • The measurement comes from a different population
  • The measurement is correct, but represents a rare event
• The interquartile range (IQR) is the distance between the lower and upper quartiles.
• A box plot's box is drawn with the ends (hinges) at the lower and upper quartiles. The median (M) is shown in the box usually by a line.
• A box plot has an inner fence marked 1.5 IQR away from the hinges. Whiskers extend from each hinge to the most extreme measurement inside the fence.
• A box plot has outer fences appearing 3 IQR from the hinges.
• Measurements falling between the inner and outer fences of a box plot are marked with a *. Measurements falling outside the outer fences is marked with a 0.
• Fill in the missing words.

  A) Lower

  B) outer

  
• Fill in the missing words.

  A) Upper

  B) outer

  
• Fill in the missing words.

  A) Lower

  B) inner

  
• Fill in the missing words.

  A) Upper

  B) inner

  
• The line (median) inside the box of a box plot represents the "center" of the distribution of data.
• The IQR of a box plot is the measure of the sample's variability.
• If one whisker in a box plot is clearly longer than the other, the distribution of the data is likely skewed in the direction of the longer whisker.
• Measurements in a box plot that fall beyond the inner fences are deemed suspect outliers.
• Measurements in a box plot that fall beyond the outer fences are considered to be highly suspect outliers.
• Observations with a magnitude of their z-score greater than 3 are considered outliers.
• Observations in highly skewed data sets with a magnitude of a z-score greater than 2 are considered possible outliers.
• An experiment is an act or process of observation that leads to a single outcome that cannot be predicted with certainty.
• A sample point is the most basic outcome of an experiment.
• The sample space of an experiment is the collection of all its sample points.
• The probability of a sample point is a number between 0 and 1 that measures the likelihood that the outcome will occur.
• The probability of a sample point can be taken to be the relative frequency.
• The probability rules for sample points:

  • All sample point probabilities must lie between 0 and 1
  • The probabilities of all the sample points within a sample space must sum to 1
• This is the symbol for the probability of sample point i.

  
• An event is a specific collection of sample points.
• The probability of an event occurring is calculated by summing the probabilities of the sample points in the sample space for that event.
• Steps for calculating probabilities of events:

  • Define the experiment (describe the process used to make an observation and the type of observation that will be recorded)
  • List the sample points
  • Assign probabilities to the sample points
  • Determine the collection of sample points contained in the event of interest
  • Sum the sample point probabilities to get the probability of the event.
• The union of 2 events is the event that occurs if either or both of the events occurs on a single performance of the experiment.
• This is the symbol for the union of 2 events.