The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is 110, not 100. The true mean and median are
a) 50.1, 52
b) 50, 52
c) 50.2, 52
d) None of these
How can you get a maximum of 110 out of 100? If it was possible, it would not change the median. Since you don't know how many scores are involved, you can't estimate the effect on the mean.
Definitely D!
50,52
To find the true mean and median after the incorrect data was discovered, we need to adjust the values and recalculate.
First, let's adjust the value of the largest item from 100 to 110. Since the original mean is 50, we can calculate the total sum of the items by multiplying the mean by the number of items: 50 * 100 = 5000.
Next, we subtract the original value of the largest item (100) and add the correct value (110) to the total sum: 5000 - 100 + 110 = 5010.
Now, we divide the new total sum by the number of items (100) to find the true mean: 5010 / 100 = 50.1.
Therefore, the true mean is 50.1.
For the median, we need to arrange the values in ascending order. Since the median is given as 52, we know that there are 50 items with values less than or equal to 52. With the adjustment of the largest item to 110, there will be 51 items with values less than or equal to the median.
Therefore, the largest value among the 51 items must be the median. As the original value was given as 100 but is now corrected to 110, the true median is 110.
Therefore, the true mean is 50.1 and the true median is 110.
Hence, the correct option is a) 50.1, 52.