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A Histogram

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  1. A Histogram

A histogram graphically presents tabulated frequencies, always shown as rectangles adjacent to each other below. Rectangles are erected in distinct intervals and have an area equivalent to the frequency of the observations. The height of each rectangle indicates the frequency density. The above data results have lengths that are repeated, which form frequencies.

The extreme lengths have minimal frequency while the highest length 300 is optimal for quality while the lengths 293, 294, 306, 307 have the lowest.

 

 

The mode is 300 =Median 300= Mean 300

A bell-shaped curve is called the standard curve or normal distribution. It is symmetrical i.e., the far left and right portions containing the low-frequency extreme scores are the tails for the distribution.

This distribution is not skewed as portrayed; it is a standard curve denoting a normal distribution since the median and mode lie at the center.

2) The specification in production is 300 +/- 5; it means the goal is 300, and parts are accepted within 295 and 305.

Calculate the Statistical Measures of Central Trend and the Statistical Measures of Spread or Dispersion and with the results decide if the process is statistically in or out of control. (25 points)

The Measures of Central Trend,

Mode, the length appearing most 300

Median The median is the score at the 50th percentile 300

Mean the mean is the score located at the mathematical center of a distribution 300

(296+279+298+299+300+301+302+303+304)/9=300

The formula for the sample mean is Sample Mean of a population

Measures of Spread or Dispersion

Measures of variability describe the extent to which scores in a distribution differ from each other.

  1. Range=maximum value¬ minimum value i.e. 305¬ 296=9

Calculate the 68%, 95.5%, and 99.7% intervals of the distribution using the Standard Normal Table and study if they are within specifications. What do you conclude about the variability of the process? (25 points)

68%= 0.68=0.47

95.5%= 0.955= 1.7

99.7%= 0.997= 2.75

The intervals of the distribution are within the specification

  Remember! This is just a sample.

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