Thinking Mathematically

Statistics:12.3 Measures of Dispersion

The RangeThe range, the difference between the highest

and lowest data values in a data set, indicates the total spread of the data.

Range = highest data value - lowest data valueExercise Set 12.3 #5

Find the range for 3, 3, 4, 4, 5, 5

Computing the Standard Deviation for a Data Set

1. Find the mean of the data items.

2. Find the deviation of each data item from the mean: data item - mean

3. Square each deviation: (data item - mean)2

4. Sum the squared deviations: add up all of the (data item - mean)2

Computing the Standard Deviation for a Data Set cont.

5. Divide the sum in step 4 by n-1, where n represents the number of data item.

6. Take the square root of the quotient in step 5. This value is the standard deviation for the data set. Standard deviation =

(data item mean)2

n 1

Example Standard Deviation

Exercise Set 12.3 #17Find the standard deviation for 1, 2, 3, 4, 5

Thinking Mathematically

Statistics:12.3 Measures of Dispersion