

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
questions, Turk ogrenciler icindir, puan amaclı, ciddiye almayın
Typology: Study notes
1 / 2
This page cannot be seen from the preview
Don't miss anything!
Measures of central tendency, or averages, are used in a variety of contexts and form the basis of statistics.
To calculate the arithmetic mean of a set of data we must first add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑^ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean (¯x).
x¯ =
∑ (^) x n
Example Find the mean of: 6, 8 , 11 , 5 , 2 , 9 , 7 , 8
x =
∑ (^) x n =
The median value of a set of data is the middle value of the ordered data. That is, the data must be put in numerical order first.
Worked examples Find the median of the following: a) 11, 4 , 9 , 7 , 10 , 5 , 6 Ordering the data gives 4 , 5 , 6 , 7 , 9 , 10 , 11 and the middle value is 7. b) 1, 3 , 0. 5 , 0. 6 , 2 , 2. 5 , 3. 1 , 2. 9 Ordering the data gives 0. 5 , 0. 6 , 1 , 2, 2.5 2. 9 , 3 , 3. 1 Here there is a middle pair 2 and 2.5. The median is between these 2 values i.e. the mean of them 2+2 2.^5 = 2. 25
In general the median is at the (n+1) 2 th value.
business www.mathcentre.ac.uk ©c mathcentre June 9, 2003
The modal value of a set of data is the most frequently occurring value.
Worked example Find the mode for: 2 , 6 , 3 , 9 , 5 , 6 , 2 , 6 It can be seen that the most frequently occurring value is 6. (There are 3 of these).
Exercises
1.5977 1.6028 1.6108 1.6067 1.5995 1.6064 1.6080 1. 1.6098 1.6049 1.6064 1.6179 1.6082 1.6095 1.
5.00 4.21 4.97 5.00 5.00 5.29 5.05 5.50 5.79 5.00 5. 5.20 5.10 5.06 4.50 4.50 5.50 4.50 5.00 5.00 5. Calculate the mean, median, and mode of this data.
Answers
business www.mathcentre.ac.uk ©c mathcentre June 9, 2003