Explain the effect of correcting the error has on the IQR and the standard deviation. The professor calculated the IQR and the standard deviation of the test scores in question 6 before realizing her mistake that is she entered the top score as 46 but it was actually 56.

Inter quartile range:
In contrast to the range, which measures only differences between the extremes, the inter quartile range (also called mid spread) is the difference between the third quartile and the first quartile. Thus, it measures the variation in the middle 50 percent of the data, and, unlike the range, is not affected by extreme values. $IQR=Q_3,-Q_1$,
Here, the IQR of the test scores is based on 50% of the observations only hence it is not affected but the standard deviation of the test scores would be affected because the mean changes which will affect the deviations and increase the standard deviation of the test scores.