from: category_eng |
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An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure? ' |
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The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is ' |
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The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is ' |
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The average (mean) of numbers is , and the average of other numbers is . What is the average of all numbers? ' |
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The Dunbar family consists of a mother, a father, and some children. The average age of the members of the family is , the father is years old, and the average age of the mother and children is . How many children are in the family? ' |
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An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure? ' |
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The minimum and maximum can be achieved with the orders and . The difference between the two is . |
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Since the average of the first numbers is , their sum is . Since the average of other numbers is , their sum is . Therefore, the average of all numbers is |
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Let be the number of children. Then the total ages of the family is , and the total number of people in the family is . So |
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Understanding |
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The minimum and maximum can be achieved with the orders and . The difference between the two is . |