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Introduction to 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…

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.

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

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

3 7 12 17 21 21 23 27 32 36 44 Data Set: Sum of the values = 243 Number of values = 11 Mean = 243 11 = 22.09 S x n x = = Mean

The most frequently occurring value in a set of data is the mode . Symbol… M Mode 27 17 12 7 21 44 23 3 36 32 21 Data Set:

3 7 12 17 21 21 23 27 32 36 44 Data Set: Mode = 21 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.” The most frequently occurring value in a set of data is the mode . Mode

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 The median is the value that occurs in the middle of a set of data that has been arranged in chronological order. 27 17 12 7 21 44 23 3 36 32 21

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 3 7 12 17 21 21 23 27 32 36 44 Data Set: Median = 21

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 3 7 12 17 21 21 23 27 32 36 44 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

0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 0 3 -1 3 2 -1 -1 1 2 -3 0 1 0 1 -2 1 2 -4 -1 1 0 -2 0 0

Specific values, called data elements , are plotted along the X-axis of the graph. Histogram 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 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 1 3 5 7 -5 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 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 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 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 Normal Distribution