a plumbing supplier's mean monthly demand for vinyl washers is 24212 with a standard deviation of 6053. The mean monthly demand for stem boilers is 6.8 with a standard deviation of 1.7. Comapre the dispersion of these distributions. Which demand pattern has more relative variation? Explain
The one for which the ratio of standard deviation to mean is highest has the largest relative variation.
In this case, they are both the same.
(std. dev.)/mean = .250 for both
Well, let me put my clown wig on and try to explain this in a funny way.
So, imagine the demand for vinyl washers is like a rollercoaster ride – sometimes it goes up, sometimes it goes down, but it usually stays within a certain range. The mean monthly demand of 24212 tells us where the rollercoaster starts, and the standard deviation of 6053 tells us how much the demand fluctuates.
On the other hand, the demand for stem boilers is like a calm, steady stream – it doesn't have as many ups and downs. The mean monthly demand of 6.8 tells us where the stream flows, and the standard deviation of 1.7 tells us how much the demand varies around that average.
Now, in terms of dispersion or relative variation, we look at how much the data spread out from the average. The higher the standard deviation, the more dispersed the data points are from the mean.
In this case, the standard deviation of 6053 for vinyl washers is much higher than the standard deviation of 1.7 for stem boilers. That tells us that the demand for vinyl washers has more relative variation – it's like a wild rollercoaster ride. On the other hand, the demand for stem boilers has less relative variation – it's more like a peaceful stream.
So, if you prefer a bit of excitement and unpredictability, go for vinyl washers. But if you prefer a calm, steady demand pattern, stem boilers are your best bet. Either way, happy plumbing adventures!
To compare the dispersion of the distributions, we can look at the relative variation, which is measured by the coefficient of variation (CV). The coefficient of variation is calculated by dividing the standard deviation by the mean and then multiplying by 100 to get a percentage.
For vinyl washers:
Mean = 24212
Standard Deviation = 6053
CV = (Standard Deviation / Mean) * 100
CV = (6053 / 24212) * 100
CV ≈ 25.00%
For stem boilers:
Mean = 6.8
Standard Deviation = 1.7
CV = (Standard Deviation / Mean) * 100
CV = (1.7 / 6.8) * 100
CV ≈ 25.00%
Both distributions have a coefficient of variation of approximately 25.00%. Therefore, they have the same relative variation.
In conclusion, the demand patterns for both vinyl washers and stem boilers have the same level of dispersion or relative variation.
To compare the dispersion of the distributions, we can use the coefficient of variation. The coefficient of variation is a measure of relative variation and is calculated as the ratio of the standard deviation to the mean, expressed as a percentage.
For the vinyl washers:
Mean = 24212
Standard Deviation = 6053
Coefficient of Variation = (Standard Deviation / Mean) * 100
= (6053 / 24212) * 100
≈ 25%
For the stem boilers:
Mean = 6.8
Standard Deviation = 1.7
Coefficient of Variation = (Standard Deviation / Mean) * 100
= (1.7 / 6.8) * 100
≈ 25%
Comparing the coefficients of variation, we can see that both the vinyl washers and stem boilers have a coefficient of variation of approximately 25%.
Therefore, both demand patterns have the same relative variation. This means that both the vinyl washers and stem boilers have a similar degree of dispersion in their demand.