The weights of 10 boxes of a children brand of cereal have a mean content of 278 grams with an S.D of 9.64 grams. If these boxes were purchased at 10 different stores and the average price per box is $ 1.29 with an S.D of $ 0.09, can you conclude that the weights are relatively more homogeneous than the prices?
The weights of 10 boxes of a children brand of cereal have a mean content of 278 grams with an S.D of 9.64 grams. If these boxes were purchased at 10 different stores and the average price per box is $ 1.29 with an S.D of $ 0.09, can you conclude that the weights are relatively more homogeneous than the prices?
To compare the homogeneity of weights and prices, we need to analyze the coefficient of variation (CV) for each variable. The CV is calculated by dividing the standard deviation (SD) by the mean and multiplying by 100.
For the weights of the cereal boxes:
CV_weights = (SD_weights / mean_weights) * 100
For the prices of the cereal boxes:
CV_prices = (SD_prices / mean_prices) * 100
Let's calculate the CV for both variables:
CV_weights = (9.64 / 278) * 100 ≈ 3.47
CV_prices = (0.09 / 1.29) * 100 ≈ 6.98
The CV for weights is 3.47%, while the CV for prices is 6.98%.
Based on these calculations, we can conclude that the weights of the cereal boxes are relatively more homogeneous than the prices. This means that the weights vary less compared to the mean weight, whereas the prices vary more compared to the mean price.
To determine whether the weights of the cereal boxes are relatively more homogeneous than the prices, we need to compare the coefficient of variation (CV) for each set of data.
The coefficient of variation is calculated as the standard deviation divided by the mean, expressed as a percentage. It provides a relative measure of dispersion that can be used to compare the variability of different sets of data.
For the weights of the cereal boxes:
Mean Content: 278 grams
Standard Deviation: 9.64 grams
CV for weights = (Standard Deviation / Mean) * 100
= (9.64 / 278) * 100
= 3.47%
For the prices of the cereal boxes:
Average Price: $1.29
Standard Deviation: $0.09
CV for prices = (Standard Deviation / Mean) * 100
= (0.09 / 1.29) * 100
= 6.98%
Comparing the coefficient of variation for weights (3.47%) and prices (6.98%), we can conclude that the weights are relatively more homogeneous than the prices. The lower CV for weights indicates that the weights of the cereal boxes have less variation compared to the prices.
Thus, based on the given data, we can conclude that the weights of the cereal boxes are relatively more homogeneous than the prices.