Using the data 29, 26, 13, 23, 23, 25, 17, 22, 17, 19, 12, 26, 30, 30, 18, 14, 12, 26, 17, 18, calculate number of observations that are two or more sample   standard deviations from the sample mean.

Sure, here are the steps to calculate the number of observations that are two or more sample standard deviations from the sample mean:

Step 1: Calculate the mean (average) of the data set. The mean is calculated by adding all the numbers in the data set and then dividing by the number of values in the set.

Step 2: Calculate the standard deviation. The standard deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma). The formula is sqrt[(Σ(xi - μ)^2 )/ n-1] where:

• Σ means "sum of"
• xi: each value from the data set
• μ: the mean
• n: the number of data points

Step 3: Identify the observations that are two or more standard deviations from the mean. This means finding the values that are below (Mean - 2Standard Deviation) or above (Mean + 2Standard Deviation).

Step 4: Count the number of these observations.

Let's calculate:

Step 1: Mean = (29+26+13+23+23+25+17+22+17+19+12+26+30+30+18+14+12+26+17+18)/20 = 21.5

Step 2: Standard Deviation = sqrt[((29-21.5)^2 + (26-21.5)^2 + (13-21.5)^2 + (23-21.5)^2 + (23-21.5)^2 + (25-21.5)^2 + (17-21.5)^2 + (22-21.5)^2 + (17-21.5)^2 + (19-21.5)^2 + (12-21.5)^2 + (26-21.5)^2 + (30-21.5)^2 + (30-21.5)^2 + (18-21.5)^2 + (14-21.5)^2 + (12-21.5)^2 + (26-21.5)^2 + (17-21.5)^2 + (18-21.5)^2 )/ (20-1)] = 6.07

Step 3: The observations that are two or more standard deviations from the mean are those below 21.5 - 26.07 = 9.36 or above 21.5 + 26.07 = 33.64.

Step 4: Looking at the data set, we see that the numbers 13, 12, 12 fall below 9.36 and the numbers 30, 30 fall above 33.64. So, there are 5 observations that are two or more sample standard deviations from the sample mean.