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.