Measures of Central Tendency

Objectives

• Calculate the mean of a set of data.• Calculate the median of a set of data.• Calculate the mode of a set of data.

Vocabulary

• central tendency• summation notation• mean• median• mode• outlier

Formulas

n

xx

n

xfx

mean of ungrouped data

mean of grouped data

Fran Tarkenton holds the all-time record in professional football for throwing touchdown passes. The number of touchdown passes (TDs) for each of his seasons is given in the table. Find the mean, median, and mode of the number of touchdown passes per year thrown by Tarkenton

Year TDs Year TDs

1961 18 1970 19

1962 22 1971 11

1963 15 1972 18

1964 22 1973 15

1965 19 1974 17

1966 17 1975 25

1967 29 1976 17

1968 21 1977 9

1969 23 1978 25

Todd Booth, an avid jogger, kept detailed records of the number of miles he ran per week during the past year. The frequency distribution summarizes his records. Find the mean, median, and mode of the number of miles per week that Todd ran.

Miles runper week

Numberof weeks

0 5

1 4

2 10

3 9

4 10

5 7

6 3

7 4

If your scores on the first four exams in a class are 73, 67, 83, and 81, what score do you need on the next exam for your overall mean to be at least 70?

The mean salary of ten employees is $28,000, and the median is $25,000. The highest paid employee gets a $5,000 raise.

a.What is the new mean salary of the ten employees?

b.What is the new median salary of the ten employees?