### 12 April (Task 2) Chap 16: Mean, Median & Mode - Let's see if I Understand...

This is a summary of the 3 types of Averages:
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Measures of Central Tendency or Averages

Arithmetic Mean
• The arithmetic mean of a set of numbers is the sum of numbers divided by the number of numbers in the set : Mean = sum of the numbers/number of numbers
• It is most the reliable measure provided there are no extreme values in the data because all the values in the data are used in calculating.
• Whenever the set of data contains extreme values, the median or mode would probably be more reliable because they are not influenced by extreme values.
Mode
• The number which occurs most frequently in a set of numbers
• It is most useful in business planning as a measure of popularity that reflects central tendency or opinion.
Median
• May be preferred as a measure of central tendency for describing economic, sociological and educational data.
• The median is popular in the study of social sciences because much of the data in the social sciences contain extreme values, in the set of household incomes.
• Median for an odd number of numbers is the middle number when the numbers are arranged in order of magnitude (i.e. ascending/descending order)
• Median for an even number of numbers is the mean of the two middle numbers when the numbers are arranged in order of magnitude
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Let's use the 3 types of averages to describe the time that S1-02 students' use of learning device after class. In total, 21 students responded.

6.5          3.5         5         4         3
5.5          9.2          1          3          2
3.5          5.5          5          7          3
3         4         5         6         3         1

1. Mean
(a) Describe how you would find the mean number of hours spend with the learning device after class.
(b) Compute the mean

2. Mode
(a) Describe how do you determine the mode of the data.
(b) What is the median number of hours?

3. Median
(a) Describe what must you do with the data before you can find the median.
(b) What is the median number of hours?

Remember to sign off with your name.

1. 1.a Add the hours then divide the number of students
1.b 4.22H(rounded off to the second decimal)
2.a Take the value that appears most frequently
2.b 3h
3.a Take the middle value
3.b 3.5H

Leighton Wang 14 s102

2. 1a. Add the total number of hours then divide by the number of students
1b. 4.2h (1 d.p.)
2a. The number that appears most frequently
2b. 3h
3a. Arrange the numbers in either ascending in descending order then use the value in the middle.
3b. 3.5h