Two filling lines produce the same central amount per bottle. Management wants a statistic that compares how steady each line is from run to run, using all observations rather than only extremes. Which measure should be reported?

Question

BlackTom AI · Accepted Answer

When deciding which statistic best captures the consistency of two filling lines across multiple runs, it’s important to consider what each measure actually summarizes.
Option a: Median. The median gives the middle value of the dataset and is robust to outliers, but it does not describe how spread out the data are from run to run. It tells you central tendency, not variability.
Option b: Mode. The mode is the most frequently occurring value. In the context of process measurements, the mode does not convey information about how much the observations vary from one run to another, so it fails to address stability across runs.
Option c: Range. The range equals the difference between the maximum and minimum values. While it indicates overall spread, it depends only on two extreme observations and ignores the entire distribution, making it a poor measure of typical run-to-run variability when many observations exist.
Option d: Standard deviation. This statistic quantifies the average deviation of each observation from the mean, effectively summarizing how tightly the data cluster around the central value. Because the goal is to compare steadiness using all observations rather than extremes, standard deviation provides a comprehensive measure of dispersion across the full dataset, reflecting run-to-run consistency.
In summary, among the given options, standard deviation is the most appropriate measure for assessing how steady each line is across runs by incorporating all observations and capturing overall variability.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

Two filling lines produce the same central amount per bottle. Management wants a statistic that compares how steady each line is from run to run, using all observations rather than only extremes. Which measure should be reported?

查看解析

登录即可查看完整答案

类似问题

Why is standard deviation a useful measure in comparing two data sets?

Question at position 48 IQs among undergraduates at Mountain Tech are approximately Normally distributed. The mean undergraduate IQ is about 110. About 95% of undergraduates have IQs between 100 and 120. The standard deviation of these IQs is about255151020

Question at position 46 If 30 is added to every number on a list, the only one of the following that is not changed isThe medianThe meanThe standard deviationThe 75th percentileThe mode

Question at position 9 ________ is a measure of dispersion that indicates how much the scores in a sample vary around the mean of the sample.RangeMedianCorrelation coefficientStandard deviation

TB MC Qu. 06-24 Of the following measures, the... Of the following measures, the best way to analyze the variability in the sample is to consider the:

位置24的问题 A stock had returns of 5 percent, 14 percent, 11 percent, −8 percent, and 6 percent over the past five years. What is the standard deviation of these returns?7.74%8.44%9.68%7.49%8.21%清除选择

A stock had returns of 16.15 percent, −6.15 percent, and 23.45 percent for the past three years. What is the standard deviation of the returns?

For some value of p, we have E[X]=11.2 and Var[X]=50.56. What is the standard deviation of (-4)*X?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单