2. You have the following marks for a math quiz: 78, 77, 82, 33, 95, 82, 71, 68, 71, 83
What are the mean median and mode
b) Two students were absent and wrote the test the next day. The new mean mark is 72. And the range is now 68. What are the marks of the two students absent?
To find the mean, median, and mode of the given marks:
Mean: To find the mean, add up all the marks and divide by the total number of marks.
78 + 77 + 82 + 33 + 95 + 82 + 71 + 68 + 71 + 83 = 720
Mean = 720 / 10 = 72
Median: The median is the middle value when the marks are arranged in ascending order.
33, 68, 71, 71, 77, 78, 82, 82, 83, 95
Since there are 10 marks, the median will be the average of the 5th and 6th value, which is (77 + 78) / 2 = 77.5
Mode: The mode is the value that appears most frequently in the set of marks.
In this case, the mode is 82 as it appears twice, which is more than any other mark.
b) To calculate the new mean and range, we need to consider the marks of the two students who were absent. Let's assume their marks are x and y.
The new mean mark is given as 72, and the total number of marks is now 12.
(78 + 77 + 82 + 33 + 95 + 82 + 71 + 68 + 71 + 83 + x + y) / 12 = 72
Rearranging the equation:
(720 + x + y) / 12 = 72
720 + x + y = 12 * 72
720 + x + y = 864
x + y = 864 - 720
x + y = 144
The range is given as 68, which is the difference between the highest and lowest marks.
To find the marks of the two students absent, we need to determine the values of x and y that satisfy the equation x + y = 144. However, without further information or constraints, there are multiple possibilities for x and y that can satisfy this equation.