Mean, Median, Mode, Range, and Standard Deviation

Descriptive statistics tell you about the distribution of data points in data set. The most common measures are the mean, median, mode, range, and standard deviation. For all the examples explained below, we will use the following fictional set of math test scores: {44, 51, 72, 72, 88, 99}. There are 6 numbers in this set, so we say n=6. Your child can work these examples out with you or a tutor.

Instructions

1. • 1、均值

     The mean of a set, or average as it is also called, is calculated by adding up all the numbers in the set, and dividing that sum by the number of entries. In our example, 44+51+72+72+88+99 = 426, and 426/6 = 71. So the mean test score is a 71.

   • 2、中位數

     The median of a set is another way of calculating a sort of "middle" value for a data set. In fact, the median is the actually the middle number when you put the data in order. In our example, we have two middle numbers, 72 and 72. If you get two middle numbers (because you have an even number of data points) just take their average (see above.)
     So we have the median score is a 72.

   • 3、众数（英语：Mode），在数学或统计学中指一组数据中出现次数最多的变量值。

     The mode is the number that occurs most frequently in a data
     set. In our example, the mode is 72. Sometimes a set can have more
     than one mode.

   • 4、范围

     The range of a set is the difference between the highest and
     lowest values. The range of scores for our imaginary students is 99-44
     = 55.

   • 5、偏差

     Standard deviation is a measure of how spread out the data
     points are. A set with a low standard deviation has most of the data
     points centered around the average. A set with a high standard
     deviation has data points that are not so clustered around the average.
     The formula for calculating SD is more complicated than the ones
     above...

   • 6、方差

     To calculate SD, first calculate the differences between
     each data point and the average. For our set, we get {27, 20, 1, 1, 17,
     28}; ignore negative signs. Then, square those numbers, so we get
     {729, 400, 1, 1, 289, 784}. Then, add them up and divide by either n-1
     or n. You divide by n-1 when your data set is a sample of a larger set,
     and you divide by n when your data set is the whole set. Let's pretend
     that ours is a sample of a larger set; so we get 440.8

   • 7、标准差

     Last step! Take the square root of 440.8, and we get 20.99.
     That means that on average, the scores are about 21 points away from
     the average.