Question

高手请进 —— 一道双语数学题

麻烦帮忙翻译一下下面的题目，如果能有详细计算过程就更好了，我会再加分。另外，是应用统计学的试题。
The Hillside Bowling Alley manager selected a random sample of his league customers. He asked them to record the number of lines they bowl during December, including league and open bowling. The reason for his interest in this data is that he is planning to offer a special discount to customers who bowl more than a specified number of games each month. The sample of eight people produced the following data.
13 32 12 9 16 17 16 12
a. Compute the mean for these sample data.
b. Compute the median for these sample data.
c. Compute the mode for these sample data.
d. Calculate the variance and the standard deviation for these sample data.
e. Note that one person bowled 32 lines. What effect, if any, does this large value have on each of the three
measures of location? Discuss.
f. For these sample data, which measure of location provides the best measure of the center of the data?
Discuss.
g. Given the sample data, suppose the manager wishes to give discounts to bowlers in the top quartile. What
should the minimum number of games bowled be in order to receive a discount?

Answer 1

第一问求的是平均数
a.mean is equal to (13+32+12+9+16+17+16+12)/8=15.875

第二问求的是中位数,需要从小到大排列后取中间的数，如果是偶数的话就是中间两个数的平均值。
b.median is the average of the 4th and 5th number in ascending order
9 12 12 13 16 16 17 32 so (13+16)/2=14.5

第三问求的是众数，就是出现次数最多的数
c.mode is 12 and 16 as it appears twice rather than others with only once.

第四问求的是方差和标准差,方差的算法是用所有的数减去平均数后平方，然后加起来再除以数量-1这里就是8个数减1，而方差是标准差的平方所以标准差就是方差开平方根
d.variance is the sum of all individual observations less mean and then divided by the number of observation minus one so variance is equal to ((9-15.875)^2+(12-15.875)^2+...+(32-15.875)^2)/(8-1)=49.554 and the standard deviation is just the square root of variance so it equal to 49.554^0.5=7.039

第五问求的是其中有个人打了32线(就是32次游戏），这是否影响前面求的三组个表示位置的数（平均数，中位数和众数）。讨论，如果不将32放在内的话，平均数就变成了13.571而中位数变成了13，众数没变。
e.If we ignore the large value 32, our mean becomes 13.571, median becomes 13 and no changes in the mode. So this means the large number 32 does issue the problem since it is too large for the sample.

第六问求的是哪个数字最能体现这组数据的中间位置或理解为中心，我认为是平均数。
f. I think mean measure the best of the center of the data.

最后一问问的是如果经理要给打的多的顾客提供折扣（前四分之一）那么打多少次才有折扣呢，前四分之一指的是按从小到大的顺序排列最后的四分之一也就是3/4处，因为这里有8个数所以是第6和第7个数的平均值。（3n+2)/4
g. If the manager wishes to give discounts to bowlers in the top quartile then the minimum number of games bowled is the average of the 6th and 7th in this sample since 8*(3n+2)/4=6.5 so in this case in order to get a discount, 16.5 number of games need to be played. It could be 16 or 17 I am not sure.^^

hope this helps
希望对你有帮助，有什么问题可以问我:)

Answer 2

麻痹
叼你吗的英语

Answer 3

半山保龄球馆经理选择了他的联赛客户随机抽样。他要求他们记录12月份创纪录的行数，他们的碗，包括保龄球联赛和开放性比赛。他对这个数据感兴趣的原因是，他计划给每个月投掷超过一个特殊数字的客户提供一个特殊的折扣。
8人的样本产生了以下数据
13 32 12 9 16 17 16 12
a，计算这些样本数据的平均数：(13+32+12+9+16+17+16+12)/8=15.875
b，从小到大排列后取中间的数，如果是偶数的话就是中间两个数的平均值：(13+16)/2=14.5
c，出现次数最多的数：12和16
d，方差和标准差,方差的算法是用所有的数减去平均数后平方，然后加起来再除以数量-1这里就是8个数减1，而方差是标准差的平方所以标准差就是方差开平方根，方差：((9-15.875)^2+(12-15.875)^2+...+(32-15.875)^2)/(8-1)=49.554 标准差：49.554½=7.039
e，有个人打了32线(就是32次游戏），这是否影响前面求的三组表示位置的数如果不将32放在内的话，平均数就变成了13.571而中位数变成了13，众数没变
f，哪个数字最能体现这组数据的中间位置或理解为中心，平均数
g，如果经理要给打的多的顾客提供折扣（前四分之一）那么打多少次才有折扣呢，前四分之一指的是按从小到大的顺序排列最后的四分之一也就是3/4处，因为这里有8个数所以是第6和第7个数的平均值