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Lesson 3, Topic 5
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# Mean, Median and Mode

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### Example:

Find the mode, median and mean of the following data:
9, 7, 5, 0, 5, 0, 3 ,0, 15, 0, 2, 2, 0, 1, 3, 5, 12, 1, 3, 2, 4

Solution:

Rearrange the numbers

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 7, 9, 12, 15

It’s obvious that 0 appears most often

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 7, 9, 12, 15

Mode = 0

The median is the 11th number

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 7, 9, 12, 15

Median = 3

Mean = $$\frac{sum\:of\:the\:given\:values}{number\:of\:values}$$

Mean =

$$\frac{0\: + \: 0 \: + \: 0 \: + \: 0\: + \: 0\: + \:1\: + \: 1\: + \: 2\: + \:2\: + \: 2\: + \: 3\: + \: 3\: + \:3\: + \: 4\: + \:5\: + \: 5\: + \: 5\: + \: 7\: + \: 9\: + \: 12\: + \: 15}{21}$$

Mean = $$\frac{79}{21}$$

Mean = 3.8

### Example:

Grace did 10 tests in English dictation and her marks were as follows:
80, 50, 60, 75, 30, 65, 60, 40, 78, 70

(i) Find her modal mark
(ii) Find her median mark
(iii) Find her mean mark

Solution:

(i) To find her Modal mark: rearrange the marks

30, 40, 50, 60, 60, 65, 70, 75, 78, 80.

The mode is 60 (60 marks occur the most)

(ii) The Median

⇒ $$\scriptsize \underset{(4 \: values)}{30, 40, 50, 60} \; \underset{(middle \: numbers)}{60,65} \; \underset{(4 \: values)}{70, 75, 78, 80}$$

Median = $$\\ \frac{sum\:of\:the\:two\:middle\:numbers}{2} \\ = \frac{60 \: + \: 65}{2}\\ = \frac{125}{2} \\ = \scriptsize 62 \frac{1}{2} \: or \: 62.5$$

(iii) The Mean

Mean = $$\frac{sum\:of\:the\:given\:values}{number\:of\:values}$$

$$=\frac{30 \:+ \:40 \:+ \:50 \: +\: 60 \:+\: 60 \:+ 65 \: + \: 70 \: + \: 75\: + \:78\: + \:80}{10}$$

Mean = $$\frac{608}{10} \\ = \scriptsize 60.8$$

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