For the following problems, recall that value = mean + (#ofSTDEVs)(standard deviation). Verify the mean and standard deviation on a calculator or computer. Note that these formulas are derived by algebraically manipulating the z-score formulas, given either parameters or statistics.
For a sample: x = + (#ofSTDEVs)(s)
For a population: x = μ + (#ofSTDEVs)(σ)
For this example, use x = + (#ofSTDEVs)(s) because the data is from a sample
Verify the mean and standard deviation on your calculator or computer.
Find the value that is one standard deviation above the mean. Find ( + 1s).
Find the value that is two standard deviations below the mean. Find ( – 2s).
Find the values that are 1.5 standard deviations from (below and above) the mean.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
1
Solution
Using the TI-83, 83+, 84, 84+ Calculator
Clear lists L1 and L2. Press STAT 4:ClrList. Enter 2nd 1 for L1, the comma (,), and
2nd 2 for L2.
Enter data into the list editor. Press STAT 1:EDIT. If necessary, clear the lists by
arrowing up into the name. Press CLEAR and arrow down.
Put the data values (9, 9.5, 10, 10.5, 11, 11.5) into list L1 and the frequencies (1, 2, 4, 4, 6, 3) into list L2. Use the arrow keys to move around.
Press STAT and arrow to CALC. Press 1:1-VarStats and enter L1 (2nd 1), L2 (2nd 2). Do not forget the comma. Press ENTER.
= 10.525.
Use Sx because this is sample data (not a population): Sx=.715891.