Numerical Mean Median Trimmed Means Standard Deviation Variance Range
Stem-and-Leaf Displays Data Format: > Numerical > At Least Two Digits Stem-and-Leaf Displays Data Format: > Numerical > At Least Two Digits
Information Conveyed: > Identification of a typical value > Extent of spread about typical value > Presence of any gaps in the data > Extent of symmetry in the distribution > Number and location of peaks > Presence of any outlying values Information Not Displayed: > Order of Observations Information Conveyed: > Identification of a typical value > Extent of spread about typical value > Presence of any gaps in the data > Extent of symmetry in the distribution > Number and location of peaks > Presence of any outlying values Information Not Displayed: > Order of Observations
Construction of Stem-and-Leaf: >Select 1 or more leading digits for stem values. The trailing digits becomes the leaves. >List possible stem values in a vertical column >Record the leaf for every observation beside the corresponding stem >Label or indicate the units for stems and leaves someplace in the display
DOTPLOTS Data Format: Numerical Distinct or Discrete Values Information Conveyed: Location Spread Extremes Gaps Construction: Each observation is a dot Stack dots above the value on a horizontal scale
Histograms (Pareto) Data Format: Qualitative (Categorical) Frequency: Number of times that a data value occurs in the data set. Relative Frequency: A proportion of time the value occurs.
Constructing a Pareto Histogram > Above each value (label), draw a rectangle whose height corresponds to the frequency or relative frequency of that value. > Ordering can be natural or arbitrary (eg. Largest to smallest).
Pareto Histogram Example During a week’s production a total of 2,000 printed circuit boards (PCBs) are manufactured. List of non-conformities: Blowholes = 120 Unwetted = 80 Insufficient solder = 440 Pinholes = 56 Shorts = 40 Unsoldered = 64 Improvements, Efforts, Time/Money?
Histograms Data Format: >Numerical >Discrete or Continuous Data displayed by magnitude. Observed frequency is a rectangle. Height corresponds to the frequency in each cell.
Histogram Construction Discrete Data: >Find Frequency of each x value >Find Relative Frequency >Mark possible x values on a horizontal scale >Above each value, draw a rectangle whose height corresponds to the frequency or relative frequency of that value
Histogram Construction Continuous Data: (Equal Widths) > Count the number of observations (n) > Find the largest & smallest (n) > Find the Range (largest- smallest) > Determine the number and width of the class intervals by the following rules:
Rules > Use from 5 to 20 intervals. Rule of Thumb: # of Intervals = √n > Use class intervals of equal width. Choose values that leave no question of the interval in which a value falls. > Choose the lower limit for the first cell by using a value that is slightly less than the smallest data value. > The class interval (width) can be determined by w = range/number of cells.
Build Histogram Continuous Data: > Tally Data for each Interval > Draw Rectangular Boxes with heights equal to the frequencies of the number of observations.
MEAN Sample Mean: _ x = Data Values n n = Number of Observations in Sample Population Mean: u = Data Values N N = Number of Objects in Population
Median Middle value after the observations are ordered from smallest to largest 50% of the values to the right. 50% of the values to the left. Odd number of samples: Middle value of the ordered arrangement. Even number of samples: Average of the two middle values.
Boxplots Information Conveyed: > Center > Spread > Nature of Symmetry > Identification of Outliers
Build Boxplots On 1. Smallest Value 2. Lower Fourth 3. Median 4. Upper Fourth 5. Largest Value Fourth Spread = Upper Fourth – Lower Fourth
Construction Of Boxplot 1. Order data from smallest to largest. 2. Separate smallest half from the largest half. (If n is odd include the median in both halves). 3. Lower fourth is the median of the smallest half. 4. Upper fourth is the median of the largest half. 5. Fourth spread = Upper fourth – Lower fourth. 6. On a horizontal measurement scale, the left edge of a rectangle is the lower fourth & the right edge is the upper fourth. 7. Place a vertical line inside the rectangle at the location of the median. 8. Draw whiskers out from ends of the rectangle to the smallest and largest data values.