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Forging new generations of engineers

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Introduction

toBasic Statistics

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Lesson Concepts Addressed

Statistical analysis of measurements

can help to verify the quality of adesign or process.

Engineers use graphics tocommunicate patterns in recorded

data.

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Related Performance Objectives

Generate a data set of linearmeasurement.

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

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S xn

x=

Mean

(pronounced X-bar)

The meanis the sum of the values of a

set of data divided by the number ofvalues in that data set.

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x= individual data value

n= # of data values in the data set

S= summation of a set of values

S xn

x=

Mean

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Data Set:

Sum of the values = 243

Number of values = 11

Mean =24311

= 22.09S xn

x= =

Mean

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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 21Data Set:

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

Mode = 21

The most frequently occurring

value in a set of data is the mode.

Mode

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Note: If two numbers of equal frequency

stand out, then the data set isbimodal. 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

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The medianis the value that

occurs in the middle of a set of datathat has been arranged in

chronological order.

Symbol x pronounced X-tilde~

Median

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Data Set:

Median = 21

Median

The medianis the value that

occurs in the middle of a set of datathat has been arranged in

chronological order.

27 17 12 7 21 44 23 3 36 32 21

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Note: A data set that contains an odd # of values

always has a Median. For an even # ofvalues, the two middle values are averaged

with the result being the Median.

Median

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Data Set:

Median = 21

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The rangeis the difference

between the largest and smallestvalues that occur in a set of data.

Range = 44-3 = 41

Symbol R

Range

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Data Set:

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A histogramis 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 histogramto showthe most common, or average, dimension that

exists among a group of identical

manufactured parts.

Histogram

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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

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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

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Large sets of data are often divided into

limited number of groups. These groups

are called classintervals.

Histogram

-5 to 5

Class In tervals

6 to 16-6 to -16

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The number of data elements is shown by

the f requency, which occurs along the Y-

axis of the graph.

Histogram

Freque

ncy

1

3

5

7

-5 to 5 6 to 16-6 to -16

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Is the data normal?

Translationdoes the greatest

frequency of the data values occur

about the mean value?

Normal Distribution

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Frequency

Data Elements

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Mean Value

Normal Distribution

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Is the process normal?

Further Translationdoes the data

form a bell shape curve when

plotted on a histogram?

Normal Distribution

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Frequency

Data Elements

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

Normal Distribution