Averages

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Average:


What is average?

Average is defined as the ratio of sum of all observations in a group to the number of observations in the group.

 

  • Average = (Sum of observations / Number of observations)
  • Suppose a man covers a certain distance at ‘a’ kmph and an equal distance at ‘b’ kmph. Then the average speed during the whole journey is 2ab/a+b

 

1. Find the average of first 20 multiples of 7.

A)    65

B)    70

C)    73.5

D)    80

E)    None of these

Explanation: Answer is C
Required Average = 7 [ (1 + 2 + 3 +…..,+20) /20 ] = [ (7*20*21)/20*2 ]=147/2=73.5

 

2. Robin scored 65, 87, 99, 45, and 79 marks (out of 100) in Math, English, Science, Hindi and Social Science. What are his average marks?

A)    69

B)    75

C)    65

D)    72

E)    None of these

Explanation: Answer is B
Average = [ (65 + 87 + 99 +45+79) /5 ]=[375/5] =75


 

3. The average of 2, 7, 6 and x is 5 and the average of 18, 1, 6, x and y is 10. What is the value of y?

A)    20

B)    15

C)    5

D)    30

E)    None of these

Explanation: Answer is C

We have = [ (2+7+6+x) /4 ]=5 or 15+x=20 or=5
Also, [ (18+1+6+x+y) /5 ]=10 or 25+5=y=50 or y=20

 

4. The average of 7 consecutive numbers is 20. The largest of these numbers is:

A)    20

B)    22

C)    23

D)    24

E)    None of these

Explanation: Answer is C
Suppose the numbers are x, x+1, x+2, x+3, x+4, x+5 and x+6.
Then, [ (x +( x+1) + (x+2) + (x+3) +(x+4) +(x+5)+(x+6) ] / 7 = 20
7x +21 = 140 => 7x = 119 => x = 17
∴ Largest Number = x + 6 => 17 + 6 = 23

 

5. A library has an average of 510 students visit on Saturdays and 240 on other days. Find the average number of students visit per day in a month of 30 days beginning with a Saturday.

A)    250

B)    276

C)    280

D)    285

E)    None of these

Explanation: Answer is D
Since the month begins with a Saturday, so there will be five Saturday in the month.
∴ Required Average = [ (510*5+240*25)/30 ] = 8550/30=285