Stats
According to the empirical rule, in a normal distribution, approximately ______% of the data lie within plus or minus 1 standard deviation of the mean, approximately ______% of the data lie within plus or minus 2 standard deviations of the mean, and approximately ______% of the data lie within plus or minus 3 standard deviations of the mean.
68% 95% 99.7%
The z-score is the number of standard deviations above or below the mean for a specified data item. So it requires dividing the difference of the mean and the data item by the standard deviation. The z-score will be positive if the data item is above the mean, negative if the data item is below the mean, and zero when the data item is equal to the mean. The formula for the z-score is given below.
Z-Score= data item-mean ------------------- standard deviation
A z-score describes how many standard deviations a data item in a normal distribution lies above or below the
mean
The difference between the highest and lowest data values in a data set is called the
range.
The standard deviation measures how much the data differ from the mean. It is symbolized either by the letter s or by the Greek letter sigma, σ.
σ. The s is used when the standard deviation of a sample is calculated. The σ is used when the standard deviation of the entire population is calculated.