up to, 1  as far as or approaching (a certain part, degree, point, etc.): She went wading up to her knees. I am up to the eighth lesson. 2  in full realization or attainment of: He worked up to president of the company. 3  as many as; to the limit of: The car will seat up to five persons.
The standard deviation is a measure of how the data is clustered about the mean. For large sets of data, approximately 68.3% of the data lies within one standard deviation of the mean and approximately 95.4% of the data lies within two standard deviations of the mean.
The standard error of the mean, also called the standard deviation of the mean, is a method used to estimate the standard deviation of a sampling distribution. To understand this, first we need to understand why a sampling distribution is required.