Find the maximum value and minimum value in milestracker. Assign the maximum value to maxmiles, and the minimum value to minmiles. Sample output for the given program: min miles: -10 max miles: 40
Answers
histogram is a specialized type of bar chart. Individual data points are grouped together in classes, so that you can get an idea of how frequently data in each class occur in the data set. High bars indicate more points in a class, and low bars indicate less points. In the histogram show above, the peak is in the 40-49 class, where there are four points.
The strength of a histogram is that it provides an easy-to-read picture of the location and variation in a data set. There are, however, two weaknesses of histograms that you should bear in mind:
The first is that histograms can be manipulated to show different pictures. If too few or too many bars are used, the histogram can be misleading. This is an area which requires some judgment, and perhaps some experimentation, based on the analyst's experience.
Histograms can also obscure the time differences among data sets. For example, if you looked at data for #births/day in the United States in 1996, you would miss any seasonal variations, e.g. peaks around the times of full moons. Likewise, in quality control, a histogram of a process run tells only one part of a long story. There is a need to keep reviewing the histograms and control charts for consecutive process runs over an extended time to gain useful knowledge about a process.
Histogram statistics:
For histograms, the following statistics are calculated:
Mean The average of all the values.
Minimum The smallest value.
Maximum The biggest value.
Std Dev An expression of how widely spread the values are around the mean.
Class Width The x-axis distance between the left and right edges of each bar in the histogram.
Number of Classes The number of bars (including zero height bars) in the histograms.
Skewness Is the histogram symmetrical? If so, Skewness is zero. If the left hand tail is longer, skewness will be negative. If the right hand tail is longer, skewness will be positive. Where skewness exists, process capability indices are suspect. For process improvement, a good rule of thumb is to look at the long tail of your distribution; that is usually where quality problems lie.
Kurtosis Kurtosis is a measure of the pointiness of a distribution. The standard normal curve has a kurtosis of zero. The Matterhorn, has negative kurtosis, while a flatter curve would have positive kurtosis. Positive kurtosis is usually more of a problem for quality control, since, with "big" tails, the process may well be wider than the spec limits.
Specification Limits and Batch Performance
Where relevant, you should display specification limits on your histograms. The specifications include a target value, an upper limit and a lower limit. For example, if Michael Jordan is shooting a basketball at a hoop, his target is the middle of the hoop. His spec limits are those points in the circle of the hoop that will just allow the ball to bounce through the basket. If the shot is outside spec limits, the ball doesn't go in.
When you overlay specification limits on a histogram, you can estimate how many items are being produced which do not meet specifications. This gives you an idea of batch performance, that is, of how the process performed during the period that you collected data. PathMaker calculates the actual percentage of items in the sample that fall outside specification limits.
When you have added target, upper and lower limit lines, you can examine your histogram to see how your process is performing.
Process.gif (2462 bytes)
If the histogram shows that your process is wider than the specification limits, then it is not presently capable of meeting your specifications. This means the variation of the process should be reduced.
Also, if the process is not centered on the target value, it may need to be adjusted so that it can, on average, hit the target value. Sometimes, the distribution of a process could fit between the specification limits if it was centered, but spreads across one of the limits because it is not centered. Again, the process needs to be adjusted so that it can hit the target value most often.
Center of a Distribution
Processes have a target value, the value that the process should be producing, where most output of the process should fall. The center of the distribution in a histogram should, in most cases, fall on or near this target value. If it does not, the process will often need to be adjusted so that the center will hit the target value.