Measures of Central Tendency And
Variation
Mean◦ Average◦ The sum of the numbers divided by the number of
numbers◦ Represented by x
Median◦ Middle number of the ordered numbers from least
to greatest◦ Mean of middle two numbers
Mode◦ The number or numbers that occur most frequently◦ There may be one mode, no mode, or more than
one mode.
Measures of Central Tendency
Range◦ Difference between the greatest and the least values.
Quartiles◦ Values that separate the data into four equal subsets, each
containing one fourth of the data. Lower Quartile
◦ It divides the lower half of the data into two equal parts. Upper Quartile
◦ It divides the upper half of the data into two equal parts. Interquartile Range (IQR)
◦ Difference between the upper and lower quartiles Outlier
◦ A value that is much less or much greater than the rest of the data.◦ Any element of a set of data that is at least 1.5 interquartile ranges
less than the lower quartile or greater than the upper quartile.
Measures of Variation
1 1 2 4 6 7 7 8 9 10 12 13 17 17 18
Measures of Variation
1 1 2 4 6 7 7 8 9 10 12 13 17 17 18
Measures of Variation
median
1 1 2 4 6 7 7 8 9 10 12 13 17 17 18
Measures of Variation
median
Lower Quartile (LQ)
1 1 2 4 6 7 7 8 9 10 12 13 17 17 18
Measures of Variation
median
Lower Quartile (LQ)
Upper Quartile (UQ)
1 1 2 4 6 7 7 8 9 10 12 13 17 17 18
Measures of Variation
median
Lower Quartile (LQ)
Upper Quartile (UQ)
UQ – LQ = IQR
1 8 9 10 10 11 12 13 13 15 27
Outlier
1 8 9 10 10 11 12 13 13 15 27
Outlier
Median
1 8 9 10 10 11 12 13 13 15 27
Outlier
MedianLQ
1 8 9 10 10 11 12 13 13 15 27
Outlier
MedianLQ UQ
1 8 9 10 10 11 12 13 13 15 27
Outlier
MedianLQ UQ
IQR = 13 – 9 = 4
1 8 9 10 10 11 12 13 13 15 27
Outlier
MedianLQ UQ
IQR = 13 – 9 = 4
9 – 1.5(4) = 3
1 8 9 10 10 11 12 13 13 15 27
Outlier
MedianLQ UQ
IQR = 13 – 9 = 4
9 – 1.5(4) = 3
Outlier
1 8 9 10 10 11 12 13 13 15 27
Outlier
MedianLQ UQ
IQR = 13 – 9 = 4
9 – 1.5(4) = 3
Outlier
13 + 1.5(4) = 19
1 8 9 10 10 11 12 13 13 15 27
Outlier
MedianLQ UQ
IQR = 13 – 9 = 4
9 – 1.5(4) = 3
Outlier
13 + 1.5(4) = 19
Outlier
Average Monthly High Temperatures (°F)
Month Honolulu
January 80.1
February 80.5
March 81.6
April 82.8
May 84.7
June 86.5
July 87.5
August 88.7
September 88.5
October 86.9
November 84.1
December 81.2
Find Measures of Central Tendency and Variation
Mean 80.1 + 80.5 + 81.6 + 82.8 + 84.7 + 86.5 + 87.5 + 88.7 + 88.5 + 86.9 + 84.1 +
81.2 12
1013.1 12
84.425
Find Measures of Central Tendency and Variation
Median80.1, 80.5, 81.2, 81.6, 82.8, 84.1, 84.7, 86.5, 86.9, 87.5, 88.5, 88.7
84.1 and 84.7
84.1 + 84.7 2
168.8 2
84.4
Find Measures of Central Tendency and Variation
ModeNo mode
Range88.7 – 80.1 = 8.6
Find Measures of Central Tendency and Variation
80.1, 80.5, 81.2, 81.6, 82.8, 84.1, 84.7, 86.5, 86.9, 87.5, 88.5, 88.7
Lower Quartile 81.2 + 81.6 = 162.8
162.8 ÷ 2 = 81.4
Upper Quartile86.9 + 87.5 = 174.4
174.4 ÷ 2 = 87.2
Find Measures of Central Tendency and Variation
IQR87.2 – 81.4 = 5.8
Outlier 81.4 – 1.5(5.8) = 72.7
87.2 + 1.5(5.8) = 95.9
No outliers
Find Measures of Central Tendency and Variation
Find the measures of central tendency and variation for the information in the table.
Guided Practice
State Area (thousand square miles)
Connecticut 6
Delaware 2
Georgia 59
Maryland 12
Massachusetts 11
New Hampshire 9
New Jersey 9
New York 54
North Carolina 54
Pennsylvania 46
Rhode Island 2
South Carolina 32
Virginia 43
Guided Practice