Page 1 - Lesson note-5-Ch 14 Statistics ( Measure of Central Tendency)

SAI International Residential School
Class –IX

Mathematics

Chapter-14: Statistics

LESSON NOTES-5

Sub topics: Measures of Central Tendency (Mean, Median and Mode)

Measures of Central Tendency

Consider a situation when two students Mary and Hary received their test copies.The
test had five questions, each carrying ten marks. Their scores were as follows:

Question Numbers 1 2 3 4 5
Mary’s score 10 8 9 8 7
Hary’s score 4 7 10 10 10

Upon getting the test copies, both of them found their average scores as follows:
Mary’s average score = 42 =8.4
5

41
Hari’s average score = =8.2
5

Since Mary’s average score was more than Harry’s, Mary claimed to have performed
better than Hary, but Hary did not agree. He arranged both their scores in ascending
order and found out the middle score as given below:
Mary’s score 7 8 8 9 10
Hari’s score 4 7 10 10 10

Harry said that since his middle-most score was 10, which was higher than Mary’s
middle-most score, that is 8, his performance should be rated better.
But Mary was not convinced. To convince Mary, Hary tried out another strategy.
He said he had scored 10 marks more often (3 times) as compared to Mary who
scored 10 marks only once. So, his performance was better.
The average score that Mary found in the first case is the mean.
The ‘middle’ score that Harry was using for his argument is the median.
The most often scored mark that Harry used in his second strategy is the mode.
There are majorly three measures of central tendency:

• Mean
• Median