How to Identify and Calculate the Mean, Median, and Mode

学生们often find that it is easy to confuse the mean, median, and mode. While all are measures of central tendency, there are important differences in what each one means and how they are calculated. Explore some useful tips to help you distinguish between the mean, median, and mode and learn how to calculate each measure correctly.

概要

为了了解平均值，中位数和模式之间的差异，首先定义术语。

• 该mean是算术大街rage of a set of given numbers.
• 该median是一组给定数字中的中间分数。
• 该modeis the most frequently occurring score in a set of given numbers.

Mean

通过增加分数并将总数除以分数来计算平均值或平均值。考虑以下数字设置：3,4,6,6,8,9,11。平均值以下列方式计算：

• 3 + 4 + 6 + 6 + 8 + 9 + 11 = 47
• 47/7 = 6.7
• 该mean (average) of the number set is 6.7.

中位数

该median is the middle score of a distribution. To calculate the median

• 以数字顺序安排您的数字。
• 计算您有多少个数字。
• 如果您有一个奇数，则将2划分为2并舍入以获得中位数的位置。
• 如果您有偶数，则除以2.转到该位置的数字，并将其平均值与下一个更高位置中的数字进行平均值以获得中位数。

Consider this set of numbers: 5, 7, 9, 9, 11. Since you have an odd number of scores, the median would be 9. You have five numbers, so you divide 5 by 2 to get 2.5, and round up to 3. The number in the third position is the median.

What happens when you have an even number of scores so there is no single middle score? Consider this set of numbers: 1, 2, 2, 4, 5, 7. Since there is an even number of scores, you need to take the average of the middle two scores, calculating their mean.

在这种情况下，平均值为2 + 4（添加两个中间数字），其等于6.然后，您需要6并将其划分为2（您在一起添加的分数总数），其等于3.因此，对于这个例子，中位数是3。

Mode

Since the mode is the most frequently occurring score in a distribution, simply select the most common score as your mode. Consider the following number distribution of 2, 3, 6, 3, 7, 5, 1, 2, 3, 9.

该mode of these numbers would be 3 since three is the most frequently occurring number. In cases where you have a very large number of scores, creating a frequency distribution can be helpful in determining the mode.

在某些数字集中，可能实际上可能是两种模式。这称为双模态分布，并且当存在频率中绑定的两个数字时发生。例如，考虑以下数量：13,17,20,21,23,23,26,29,30。在该组中，两个和23都发生两次。

应用程序

How do you determine whether to use the mean, median, or mode? Each measure of central tendency has its own strengths and weaknesses, so the one you choose to use may depend largely on the unique situation and how you are trying to express your data.

• 该mean utilizes all numbers in a set to express the measure of central tendency; however, outliers can distort the overall measure. For example, a couple of extremely high scores can skew the mean so that the average score appears much higher than most of the scores actually are.
• 中位数摆脱了不成比例的高或低分，但它可能无法充分代表全套数字。
• 该模式可能对异常值的影响较小，并且擅长表示给定数量组的“典型”，但在不超过一次的情况下可能不太有用。

想象一下，房地产经纪人想要衡量她在去年销售的房屋中央趋势的情况。她列出了所有总数的清单：

• 75,000美元
• 75,000美元
• 150,000美元
• 155,000美元
• 165,000美元
• 203,000美元
• $750,000
• $755,000

该集团的平均值为291,000美元，中位数为160,000美元，模式为75,000美元。您会说哪种销售数字集中趋势的最佳衡量标准？如果它们想要最高数量，均值显然是最佳选择，即使总体偏斜两个非常高的数字。

然而，该模式不会是一个不错的选择，因为它不成比例低，而不是她对年度销售的良好代表。另一方面，中位数似乎是她房地产上的“典型”销售价格的相当良好的指标。