如何正确求解给定百分比数据集的均值？已尝试AVERAGE、IQR及T统计量未果

Hey there! Let's walk through this problem together to figure out the best way to calculate the mean for your percentage dataset. First, let's recap your data to make sure we're on the same page:

-36.64% -47.15% 112.43% -5.25% 35.08% 30.17% 38.05% 5.70% -21.85% -18.04% 2.73% 0.24% 8.36% 117.35% -40.26% -15.71% -4.01% 6.24% -57.36% -18.74% 182.71% -83.38%

You tried three tools: AVERAGE (arithmetic mean), IQR, and T-statistic. Let's break down what each is for, and why they aren't all giving you a "single correct answer":

1. Arithmetic Mean (AVERAGE Function) #

First, let's calculate this properly: adding all 22 values and dividing by 22 gives an arithmetic mean of ≈8.67%. But here's the catch: your dataset has extreme outliers (like 182.71%, -83.38%, 112.43%, and 117.35%) that pull this mean upward. For most cases, this number doesn't reflect the "typical" value in your dataset—since most values are between -57% and 38%.

2. IQR (Interquartile Range) #

IQR isn't a mean calculation method—it's a tool to identify outliers. Here's how to use it for your data:

• Sort the dataset, then find Q1 (25th percentile: ≈-29.25%) and Q3 (75th percentile: ≈19.27%)
• IQR = Q3 - Q1 = 48.51%
• Outliers are values below Q1 - 1.5IQR (-102.01%) or above Q3 + 1.5IQR (92.03%)
• This flags three outliers: 112.43%, 117.35%, 182.71%

Once you identify outliers, you can choose to exclude them and recalculate the mean. Excluding these three gives a trimmed mean of ≈-11.67%—a huge difference from the arithmetic mean!

3. T-Statistic #

The T-statistic isn't used to calculate a mean—it's for hypothesis testing (e.g., "Is my sample mean significantly different from a hypothesized population mean?"). So this tool was misapplied here; it won't help you find the "best" mean, but it can help you analyze the significance of whatever mean you choose.

There's no universal "correct" mean—it depends on what you're trying to measure:

If you need to include all data (even extreme values) #

• Use the arithmetic mean (≈8.67%), but pair it with the median (≈-1.89%) and standard deviation to show how spread out the data is. This is useful if those outliers are real, important events (like a one-time huge profit or loss that you need to account for in overall averages).

If you want a "typical" value (ignoring outliers) #

• Median (≈-1.89%): This is the middle value when sorted, and it's completely unaffected by extreme outliers. It's great for skewed datasets like yours.
• Trimmed Mean: Exclude a fixed percentage of extreme values (we excluded ~14% here, the three top outliers) to balance between including most data and reducing outlier impact. The result (~-11.67%) is more representative of the bulk of your data.

What to avoid: Geometric Mean #

You might wonder about this, but geometric mean works for positive growth rates—your dataset has negative values, so it's not applicable here (you can't take the root of a negative number).

1. Visualize your data: Make a box plot to see the spread and outliers clearly—this will help you justify your choice of mean.
2. Decide if outliers matter: If those extreme gains/losses are one-off events or data errors, exclude them and use the trimmed mean or median. If they're legitimate and important to your analysis, stick with the arithmetic mean and note the outliers' impact.
3. Report context: Always explain which mean you used and why—this makes your analysis transparent to others.

内容的提问来源于stack exchange，提问作者user13024918