In this note, you will find information explaining why we need data, but also how to collect and process it.

Information: click the arrow to view the information

• Why do we need data?

  • Data is used throughout the Engineering Design Process to optimize designs and improve efficiency during production

  • Statistics refer to the collection and organization of data(science) as well as the analysis and presentation of those data(mathematics)

  • Statistics are often evaluated using the assistance of computers and software such as Microsoft Excel

  • Such tools allow user to easily access, collect, organize, maintain, manipulate, and interpret data – which helps to improve efficiency

Basic Statistics Vocabulary:

• Mean - the average of a given data set

• Median - the middle number in a given ordered set

• Mode - the most frequently occurring number in a given data set

• Standard Deviation - how much variation exists from the average(mean) in a given data set

• Range - the distribution of the data set or the difference between the largest and smallest values

• Tolerance - the amount of characteristic(product/part/dimension/etc) can vary without compromising(affecting) the overall function or design of the product

• Normal size - the size used in the general description of a part/product

• Basic size - the converted normal size(fraction to decimal) that can produce some deviation

• Upper Specification Limit - the highest acceptable deviation or value for a characteristic

• Lower Specification Limit - the lowest acceptable deviation or value for a characteristic

• Mean - the average of a given data set:

  • x = represents the data set

  • ∑ = the sum of a mathematical operation

  • n = the total number of variables in the data set

  • Equation for mean =     ∑x/n

    • Add the numbers in the data set first, then divide the product by the number of variables

• Median - the middle number in a given ordered data set

  • If the given data set has an even number of data, the median is the average of the two center data

    • Add the two numbers together then divide the product by 2

• Mode - the most frequently occurring number in a given data set

• Standard Deviation - Standard Deviation (SD) is a UNIT. It is used to measure the variability of individual data to the mean.

  • The smallest value that the standard deviation can be is 0. Standard deviation can not be negative.

    • Standard Deviation Steps Explained:

      • The mean must first be found through adding all numbers in a data set, and dividing by the pieces of data within the data set.

      • Subtract the mean from each value

      • Square the differences

      • Find the average of the squared numbers to find the variance

      • Square the variance to find the standard deviation

    • Calculating Standard Deviation

      • Equation for Standard Deviation  =  ∑(xi – μ)²

    √     n - 1

    • xi = represents the individual data

    • μ = represents the mean of the data set

    • ∑ = the sum of a mathematical operation

    • n = the total number of variables in the data set

    • The range is the distribution of the data set or the difference between the largest and smallest values in a data set

• Engineering tolerance is the amount a characteristic can vary without compromising the overall function or design of the product.

• Tolerances generally apply to the following:

  • Physical dimensions (part and/or fastener)

  • Physical properties (materials, services, systems)

  • Calculated values (temperature, packaging)

• American National Standards Institute (ANSI) standards.

  • Examples:

    • Bilateral Tolerance (1.125  0.025)

    • Unilateral Tolerance (2.575)