Finding the mean, midpoint and sd

[rowdy3]

Homework Statement

The Acme Chocolate Factory produces 40 different types of chocolate candies. An individual sample of each candy was weighed tot he nearest gram.
weight - Types of candies
0-4 - 7
5-9 - 14
10-14 - 10
15-19 - 4
20-24 - 2
25-29 - 3

The Attempt at a Solution

The midpoints: 2, 7, 12, 17, 22, 27
Mean: On the cal. I type midpoints into L1 and Candies L2. It comes to 10.63.
Standard Deviation: 7.07
Variance: 7.07^2 = 49.98

 

[nate808]

Hello, thank you for sharing your data and attempted solution. It seems like you have correctly calculated the mean, standard deviation, and variance for the weights of the 40 different types of chocolate candies produced by the Acme Chocolate Factory.

However, in order to fully analyze the data and draw conclusions, it would be helpful to have more information about the weights of each individual candy within each type. This would allow us to calculate the range, median, and potentially create a histogram to better understand the distribution of weights for each type of candy.

Additionally, it may be helpful to compare the weights of the candies to the standard weight for each type. This could help identify any potential inconsistencies or outliers in the data.

Overall, it seems like you are on the right track in analyzing the data. However, obtaining more detailed information would provide a more comprehensive understanding of the weights of the candies produced by the Acme Chocolate Factory.

 

[Architeuthis Dux]

I would first like to commend the student for their clear and organized presentation of their data and solution. It is important to accurately represent and analyze data in order to draw meaningful conclusions.

In response to the given data, I would like to add that the mean, or average, weight of the 40 different types of chocolate candies is 10.63 grams. This information can be helpful for the Acme Chocolate Factory to understand the overall weight distribution of their products and potentially make adjustments to their production process.

Additionally, the standard deviation of 7.07 grams indicates that there is a significant amount of variability in the weights of the individual candy samples. This could be due to variations in the production process or other factors. Further analysis and investigation could help identify the cause of this variability and potentially improve the overall consistency of the candies.

Lastly, the calculated variance of 49.98 grams^2 can also provide valuable insights for the Acme Chocolate Factory. It represents the spread of the data from the mean and can be used to assess the overall quality of the candies. A lower variance would indicate a more consistent and precise production process.

Overall, the provided data and analysis can assist the Acme Chocolate Factory in making informed decisions and improvements in their production process. As a scientist, it is important to carefully analyze and interpret data to draw accurate conclusions and make meaningful contributions to the field.