英语的统计学问题,有关标准差、平均值

题目

英语的统计学问题,有关标准差、平均值
 A group of 13 students is studying in Istanbul,Turkey,for five weeks.As part of their study of the local 
economy,they each purchased an Oriental rug and arranged for its shipment back to the United States.The
shipping time,in days,For each rug was 
31     31     42     39      42     43      34    
30     28      36     37     35     40  
Estimate the percentage of days that are within two standard deviations of the Mean.Is it likely to take 2 
months for a delivery? 





Estimate the percentage of days that are within two standard deviations of the Mean.

请写出具体的计算步骤

答案

估计有多少百分比的数据是在是在两个平均标准差之内
1.先计算平均值(mean):(31+31+42+39+42+43+34+30+28+36+37+35+40)/13=36
2.计算变异量/方差(variance):即(数据值-平均值)^2 以第一个为例:31-36 = -5 然後平方之 = 25
25 25 36 9 36 49 4
36 64 0 1 1 16
3.计算平均标准差(SD):
a把所有方差(variance) 的总和开方(sqrt)
b方差总和是 25+25+36+9+36+49+4+36+64+0+1+1+16 = 302
c开方(sqrt)302= 17.38
d再把开方结果除13(学生数):17.38/13= 1.34,1.34就是平均标准差(standard deviation)
4两个平均标准差之内的数值为:(36-2X1.34)和(36+2X1.34)之间,即33.32到38.68之间
合符的有34 36 37 35 四个
计算答案百分比:4/13*100% = 30.76%