Question

5. Find the mean, median and mode of the given data. 7, 8, 12, 10, 9, 8, 9, 11, 8, 11, 8

Answer 1

Answer :

• Mean = 9.1
• Median = 8.5
• Mode = 8

Given :

• 7 , 8 , 12 , 10 , 9 , 8 , 9 , 11 , 8 , 11 , 8

To find :

• Mean
• Median
• Mode

Solution :

Mean :

• 7 , 8 , 12 , 10 , 9 , 8 , 9 , 11 , 8 , 11 , 8

We know that :

• Mean = Sum of observations/Number of observations

Where,

• Sum of observations is 7 , 8 , 12 , 10 , 9 , 8 , 9 , 11 , 8 , 11 , 8
• Number of observations is 11

↬ Mean = sum of observations / Number of observations

↬ Mean = 7 + 8 + 12 + 10 + 9 + 8 + 9 + 11 + 8 + 11 + 8 / 11

↬ Mean = 101/11

↬ Mean = 9.1

Hence, Mean is 9.1

Median :

We know that,

• Median = (n/2)th observation + (n/2 + 1)th observation

where,

• n is 11

↬ Median = (n/2)th observation + (n/2 + 1)th observation

↬ Median = (11/2)th observation + (11/2 + 1)th observation

↬ Median = 5th observation + 6th observation / 2

Ascending order : 7 , 8 , 8 , 8 , 8 , 9 ,9 , 10 , 11 , 11 , 12

↬ Median 8 + 9 / 2

↬ Median = 17/2

↬ Median = 8.5

Hence, Median is 8.5

Mode :

↬11 occurs twice and 8 occurs 4 times so,

Hence , Mode is 8.

• Mean = 9.1
• Median = 8.5
• Mode = 8