1. 7.3 Find Measures of Central Tendency and Dispersion

2. Vocabulary
Statistics: numerical values used to summarize and compare sets of data
Measure of central tendency: number used to represent the center or middle set of data
Mean the average
Median – the middle number
Mode – number that occurs most

3. Vocabulary
Measure of Dispersion: statistic that tells you how spread out the values are
Range – biggest - smallest
Standard Deviation: “sigma”

4. EXAMPLE 1
Find measures of central tendency
Waiting Times
The data sets at the right give the waiting times (in minutes) of several people at two veterinary offices. Find the mean, median, and mode of each data set.
SOLUTION
Office A: Mean: x = 9 … 9
198 = 22 =
Median: 20 Mode: 24 9
Office B: Mean: x = … 9 =
144 = 16
Median: 18 Mode: 18

5. GUIDED PRACTICE
for Example 1
TRANSPORTATION 1.
The data set below gives the waiting times (in minutes) of 10 students waiting for a bus. Find the mean, median, and mode of the data set.
4, 8, 12, 15, 3, 2, 6, 9, 8, 7
SOLUTION
Mean: x = 10 … 10 = 74 =
7.4
Median: Mode: 8

6. EXAMPLE 2
Find ranges of data sets
Find the range of the waiting times in each data set. Explain what that means.
SOLUTION
= 18
Office A: Range = 32 – 14
Office B: Range = 23 – 8
= 15
Because the range for office A is greater, its waiting times are more spread out.

7. EXAMPLE 3
Standardized Test Practice
( )2 –
+ ( )2 –
( )2
... – =
290 9
Office A: =
5.7 9
Office B: =
(8 16)2 + (11 16) (23 16)2 –
... 9 =
182 9
4.5
ANSWER
The correct answer is D.

8. GUIDED PRACTICE
for Examples 2 and 3
Find the range and standard deviation of the data set.
4, 8, 12, 15, 3, 2, 6, 9, 8, 7
Range = 15 – 2
SOLUTION
= 13
= 3.8
Standard deviation