分类变量标准差及1-10分问卷数据标准差计算方法咨询

Hey there, let's walk through exactly how to compute the sample standard deviation when you have N participants answering a survey question on a 1-10 scale. This is a super common use case, so here's the step-by-step breakdown that's easy to follow:

• First, calculate the mean of all responses: Add up every participant's score (from 1 to 10) and divide that total by the number of participants, N.
• For each participant's response (let's call this the i-th observation), find its deviation from the mean: subtract the mean you just calculated from their individual score. Then square this deviation to get the squared deviation from the mean—this step gets rid of negative values so differences don't cancel each other out.
• Sum up all these squared deviation values across every single participant.
• Divide that total sum by N-1 (this is crucial for sample standard deviation; using N-1 instead of N adjusts for bias since we're working with a sample of data, not the entire population).
• Take the square root of that final quotient, and you'll have your sample standard deviation.

A quick side note: Even though a 1-10 scale is technically ordinal categorical data, it's standard practice to calculate standard deviation here because the scale has equal, meaningful intervals between each point, letting us treat it like interval data for this statistical calculation.

内容的提问来源于stack exchange，提问作者Gabriel