Question

A manager examines the histogram below and, after conducting additional research, finds that the observation in bin 3 is an input error and should have been entered as 13. If the histogram is updated with the correct number, which of the following will occur?

1) The mean will decrease.
2) The mode will increase.
3) The median will increase.
4) The standard deviation will decrease.

Answer 1

The question addresses the effects on statistical measures like mean, median, mode, and standard deviation after correcting an erroneous data entry in a histogram.

Step-by-step explanation:

The question is concerned with the impact on statistical measures after correcting an input error in a dataset. A correct observation of 13, instead of an erroneous entry in bin 3 of a histogram, likely causes changes to the mean, median, mode, and standard deviation. Given the situation, the following changes can be expected after the correction:

1. The mean will potentially decrease if the incorrect value was above 13.
2. The mode will not change as it is the value that appears most frequently and is not affected by a singular data correction unless the wrong value was also the mode.
3. The median may increase if the incorrect value was included in the calculation of the median before, and it was less than the value of the corrected data point. However, this also depends on the position of the 13 in respect to the other values.
4. The standard deviation measures the spread of data around the mean. If the incorrect value was causing a distortion in this spread, correcting it to 13 could decrease the standard deviation if the error resulted in a higher deviation than with the correct value.

It is important to note that these changes are contingent on the position and influence of the incorrect data point within the set of observations. In a normal distribution, the mean, median, and mode coincide, and changes to data points can shift these values accordingly.