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Introductionto Basic Statistics

Lesson Concepts Addressed Statistical analysis of measurements can help to verify the quality of a design or process. Engineers use graphics to communicate patterns in recorded data.

Related Performance Objectives Generate a data set of linear measurement. Calculate the mean, mode, median, and range of a data set. Create a histogram of recorded measurements showing class interval and frequency. It is expected that students will…

S xS x n x = Mean (pronounced “X-bar”) mean The mean is the sum of the values of a set of data divided by the number of values in that data set.

x = individual data value n = # of data values in the data set S = summation of a set of values S xS x n x = Mean

Data Set: Sum of the values = 243 Number of values = 11 Mean = = S xS x n x = = Mean

mode The most frequently occurring value in a set of data is the mode. Symbol… M Mode Data Set:

Data Set: Mode = 21 mode The most frequently occurring value in a set of data is the mode. Mode

Note:If two numbers of equal frequency stand out, then the data set is “bimodal.” If more than two numbers of equal frequency stand out, then the data set is “multi-modal.” mode The most frequently occurring value in a set of data is the mode. Mode

median The median is the value that occurs in the middle of a set of data that has been arranged in chronological order. Symbol… x pronounced “X-tilde” ~ Median

Data Set: Median = 21 Median median The median is the value that occurs in the middle of a set of data that has been arranged in chronological order

Note:A data set that contains an odd # of values always has a Median. For an even # of values, the two middle values are averaged with the result being the Median. Median Data Set: Median = 21

range The range is the difference between the largest and smallest values that occur in a set of data. Range = 44-3 = 41 Symbol… R Range Data Set:

A histogram is a common data distribution graph that is used to show the frequency with which specific values, or values within ranges, occur in a set of data. An engineer might use a histogram to show the most common, or average, dimension that exists among a group of identical manufactured parts. Histogram

Specific values, called data elements, are plotted along the X-axis of the graph. Histogram Data Elements

Large sets of data are often divided into limited number of groups. These groups are called class intervals. Histogram -5 to 5 Class Intervals 6 to 16-6 to -16

The number of data elements is shown by the frequency, which occurs along the Y- axis of the graph. Histogram Frequency to 5 6 to 16-6 to -16

“Is the data normal?” Translation…does the greatest frequency of the data values occur about the mean value? Normal Distribution

Frequency Data Elements Mean Value Normal Distribution

“Is the process normal?” Further Translation…does the data form a bell shape curve when plotted on a histogram? Normal Distribution

Frequency Data Elements Normal Distribution