英文回答：
Standard deviation and variance are two commonly used statistical measures that help us understand the spread or dispersion of a set of data points.
Variance is a measure of how spread out the data points are from the mean or average. It is calculated by taking the average of the squared differences between each data point and the mean. In other words, variance measures the average of the squared deviations from the mean.
For example, let's say we have a set of exam scores: 80, 85, 90, 95, and 100. To calculate the variance, we first find the mean, which is (80+85+90+95+100)/5 = 90. Then, we calculate the squared differences from the mean for each data point: (80-90)^2, (85-90)^2, (90-90)^2, (95-90)^2, and (100-90)^2. Taking the average of these squared differences gives us the variance.
Standard deviation, on the other hand, is the square root of the variance. It measures the average amount by which each data point differs from the mean. Standard deviation is often preferred over variance because it is in the same units as the original data points, making it easier to interpret.
Continuing with our example, once we have calculated the variance, we can find the standard deviation by taking the square root of the variance. In this case, let's say the variance is 50. The standard deviation would then be the square root of 50, which is approximately 7.07.
In summary, variance measures the average of the squared deviations from the mean, while standard deviation measures the average amount by which each data point differs from the mean.
中文回答：
标准差和方差是两个常用的统计量，帮助我们了解一组数据点的分散程度。
举个例子，假设我们有一组考试分数，80、85、90、95和100。为了计算方差，我们首先到均值，即（80+85+90+95+100）/5 = 90。然后，计算每个数据点与均值之间的差值的平方，（80-90）^2、（85-90）^2、（90-90）^2、（95-90）^2和（100-90）^2。将这些平方差的平均值得到方差。
而标准差则是方差的平方根。它衡量了每个数据点与均值之间的平均差异程度。标准差通常比方差更受青睐，因为它与原始数据点具有相同的单位，更容易解释。
继续以上面的例子，一旦我们计算出方差，就可以通过求方差的平方根来得到标准差。假设方差为50，则标准差为50的平方根，约为7.07。
总结一下，方差衡量了与均值的平方差的平均值，而标准差则衡量了每个数据点与均值之间的平均差异程度。
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