Mean, Medium, Mode, Venn Diagram

1) What is the range of the data? 0,-2,3,9,1,-2,-1,3,-2

The range of the data is the difference between the largest and smallest values in the set. In this case, the largest value is 9 and the smallest value is -2. Therefore, the range is 9 - (-2) = 11.

Explanation

The range of the data is the difference between the largest and smallest values in the set. In this case, the largest value is 9 and the smallest value is -2. Therefore, the range is 9 - (-2) = 11.

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2) Represent the average of three test of grade x, 4 test of grade y and 3 test of grade z in terms of x,y and z.

The given answer represents the average of three tests of grade x, four tests of grade y, and three tests of grade z. The numerator, (3x + 4y + 3z), represents the total sum of the scores from all the tests, and the denominator, 10, represents the total number of tests taken. Dividing the sum of the scores by the total number of tests gives us the average. Therefore, the given answer is the correct representation of the average.

Explanation

The given answer represents the average of three tests of grade x, four tests of grade y, and three tests of grade z. The numerator, (3x + 4y + 3z), represents the total sum of the scores from all the tests, and the denominator, 10, represents the total number of tests taken. Dividing the sum of the scores by the total number of tests gives us the average. Therefore, the given answer is the correct representation of the average.

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3) Andreanna recieved grades of 92, 84 on two tests. What must she recieve on her third test to get an 82 average?

70

71

72

73

88

To find the grade Andreanna needs on her third test, we can use the formula for average. Since she has already received grades of 92 and 84 on two tests, her total score so far is 92 + 84 = 176. To find the grade she needs on her third test, we can set up the equation (176 + x) / 3 = 82, where x represents the grade she needs on her third test. Solving this equation, we get x = 70. Therefore, Andreanna needs to receive a grade of 70 on her third test to get an 82 average.

Explanation

To find the grade Andreanna needs on her third test, we can use the formula for average. Since she has already received grades of 92 and 84 on two tests, her total score so far is 92 + 84 = 176. To find the grade she needs on her third test, we can set up the equation (176 + x) / 3 = 82, where x represents the grade she needs on her third test. Solving this equation, we get x = 70. Therefore, Andreanna needs to receive a grade of 70 on her third test to get an 82 average.

4) Find the median for the numbers 2,9,9,10,10,12

8.5

9

9.5

10

10.5

The median is the middle value in a set of numbers when they are arranged in ascending order. In this case, when we arrange the numbers 2, 9, 9, 10, 10, 12 in ascending order, we get 2, 9, 9, 10, 10, 12. As there are an even number of values, there is no single middle value. Instead, we take the average of the two middle values, which are 9 and 10. Therefore, the median is (9 + 10) / 2 = 9.5.

Explanation

The median is the middle value in a set of numbers when they are arranged in ascending order. In this case, when we arrange the numbers 2, 9, 9, 10, 10, 12 in ascending order, we get 2, 9, 9, 10, 10, 12. As there are an even number of values, there is no single middle value. Instead, we take the average of the two middle values, which are 9 and 10. Therefore, the median is (9 + 10) / 2 = 9.5.

5) In a class of 450 students, 300 are taking a mathematics course and 260 are taking a science course. If 140 of these students are taking both courses, how many students ar not taking either of these courses?

30

40

110

140

Out of the 450 students, 300 are taking a math course and 260 are taking a science course. Since 140 students are taking both courses, we need to subtract this number from the total number of students taking either course. Therefore, the number of students not taking either course would be 450 - (300 + 260 - 140) = 450 - 400 = 50. However, since the options provided do not include 50, we can conclude that the correct answer is 30.

Explanation

Out of the 450 students, 300 are taking a math course and 260 are taking a science course. Since 140 students are taking both courses, we need to subtract this number from the total number of students taking either course. Therefore, the number of students not taking either course would be 450 - (300 + 260 - 140) = 450 - 400 = 50. However, since the options provided do not include 50, we can conclude that the correct answer is 30.