1. Measures of Central Tendency
Section 5.1
Standard: MM2D1 bc
Essential Question: How do I calculate and use measures of central tendency and dispersion to compare data sets?

2. Statistics: numerical values used to summarize and compare sets of data
Mean: average, denoted by
Median: the middle number when the numbers are in order
Mode: the number or numbers that occur more frequently
Measures of dispersion: a statistic that tells you how spread out the data values are
Range: the difference between the greatest and least data values
Standard deviation: the measure that describes the typical difference between a data value and the mean, denoted by σ
Interquartile range: the difference between the upper and lower quartile of a set of data
Variance: standard deviation squared.

3. Find the following. 1. 42, 78, 56, 95, 49, 55, 63, 71 Mean: _______
Median: _______
Mode: _______
Range: _______
Q1: _______
Q2: _______
Q3: _______
IQR: _______
63.63
= 509
509/8  63.63
59.5
42, 49, 55, 56, 63, 71, 78, 95
none 53
95 – 42 Q1
( )/2 52
Median
( )/2
59.5 Q2 Q3
( )/2
74.5 52
59.5
74.5
22.5
74.5 – 52

4. Standard deviation of population σ (read as “sigma”) of x1, x2, …, xn is:
Now find the standard deviation of example 1:
42, 78, 56, 95, 49, 55, 63, 71

6. Standard Deviation on the Calculator:
2nd DATA ENTER (1-VAR)
DATA
Input data into x1, x2, x3, …
Use to move to next data entry
Notice there is a FRQ after each xn term. This is means frequency. If a number appears in the list more than once you may change this to the number of times the number appears in the list.
STATVAR
n = number of terms • = mean
Sx = sample stand. dev. • σx = population stand. dev.
Σx = sum of data • Σx2 = sum of data squared

7. 2. 15, 11, 15, 14, 14, 13, 17
Mean: _______
Median: _______
Mode: _______
Range: _______
Q1: _______
Q2: _______
Q3: _______
IQR: _______
Standard deviation: _______
Variance: ______
14.14
= 99
99/7 = 14.14 14
11, 13, 14, 14, 15, 15, 17
14, 15 6
17 – 11 Q1 13
Median 14 Q2 Q3 15 13 14 15 2
15 – 13
1.73
2.98
(Standard deviation)2

8. Draw a box and whisker plot for the data set.
Now check for outliers. (Remember: 1.5 • IQR)
1.5(2) = 3
Q3 + 3 = = 18 (No values larger than 18)
Q1 – 2 = 13 – 3 = 10 (No values smaller than 10)
Therefore, no outliers.

9. 3. Compare the means and standard deviations of Set A and Set B.
Set A mean: _______ Set B mean: _______
standard deviation: _______ standard deviation: _______
Set A 7 3 4 9 2
Set B 5 8 6 5 6
2.6
1.4
Set B has a higher average and Set A’s data is more spread out.

10. 4. The lists show the number of cars sold each month for one year by two competing car dealers. Compare the mean and standard deviation for the numbers of cars sold by the two car dealers.
Dealer A: 8, 9, 15, 25, 28, 16, 24, 18, 21, 14, 16, 10
Dealer B: 7, 4, 10, 18, 21, 30, 27, 20, 16, 18, 12, 9
Dealer A mean: _______ Dealer B mean: _______
standard deviation: _______ standard deviation: _______ 17 16
6.2
7.6
Dealer A sells more cars on average and Dealer B’s data is more spread out.