Lee took a survey for the school newspaper and received the following data about the number of hours classmates studied per week: (1,2,4,5,6,8,9,10,10). Express as a common fraction the positive difference between tthe median and mean of this set of data.
To find the mean, add the numbers and divide by 9.
To find the median, find the number in the middle.
Find the mean (average)
1 + 2 + 4 + 5 + 6 + 8 + 9 + 10 + 10 = sum
Average = sum/9
The median is the middle value, 6
mean - median = postive difference
Then express this difference as a fraction
To find the median and mean of the given data set, follow these steps:
Step 1: Sort the data in ascending order.
(1, 2, 4, 5, 6, 8, 9, 10, 10)
Step 2: Find the median.
Since there are nine numbers in the data set, the median will be the middle number. In this case, the median is 6.
Step 3: Find the mean.
To find the mean, sum up all the numbers in the data set and divide by the total number of values. In this case, the sum is 55 (1 + 2 + 4 + 5 + 6 + 8 + 9 + 10 + 10 = 55), and the total number of values is 9. So, the mean is 55/9, which simplifies to 6 1/9.
Step 4: Calculate the positive difference between the median and mean.
To find the positive difference, subtract the mean from the median. In this case, the positive difference is 6 - 6 1/9.
To express the difference as a common fraction, we can write 6 as 6/1 and subtract it from 6 1/9, which can be written as 55/9.
Therefore, the positive difference between the median and mean is 55/9 - 6/1.
To simplify the expression, find a common denominator for 9 and 1, which is 9. So, the fraction becomes:
(55/9) - (6/1) = (55/9) - (54/9) = 1/9.
Hence, the positive difference between the median and mean is 1/9 in common fraction form.