ABPS AVERAGE - ASSIGNMENT

                             ABPS Average-Assignment 

1)The average of 7 consecutive numbers is 20. What is the largest of these numbers?

A) 23

B) 27

C) 25

D) 29

Ans - 

The average of 7 consecutive numbers i.e. 20 is the median of it.

Hence 7 consecutive numbers respectively

17, 18, 19, 20, 21, 22, 23

↓

         Median Number

Hence the largest number is 23.

2)What is the average of natural numbers from 1 to 67?

A) 36

B) 42

C) 40

D) 34

Ans-

Average = n+1/2

Given, natural numbers from 1 to 67

n = 67

Therefore,

Average = 67+1/2

Average=68/2

Average= 34

Thus, average of natural numbers from 1 to 67 is 34.

3)The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?

Ans-

if we add 9 numbers =9*9=81

first 5 numbers added to 10*5=50

last 5 numbers added to 8*5=40

If we add last two conditions total is 50+40=90

here all 9 numbers are added and also 5th number once more added

so 5th observation is 90-81=9.

4) The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?

A) 23

B) 25

C) 29

D) 27

Ans- 

Average of 10 numbers = 23

Sum/Total numbers = 23

Sum/10 = 23

Sum of the 10 numbers = 230

If each number is increased by 4, the total increase = 4 x 10 = 40

New sum = 230+40= 270

Therefore, the new average-

270/10= 27

5) A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

A) RS. 5991

B) RS. 4551

C) RS. 4991

D) RS. 6991

Ans - 

Step-1: Finding the sum of sales of

We have, Five consecutive months salary = Rs. 6435, Rs. 6927, Rs. 6855,

Rs. 7230, Rs. 6562.

Let sale of sixth month be Rs X.

Therefore, sum of six consecutive month = Rs.

(6435+ 6927 + 6855 + 7230 + 6562 + x)=

Sum of six consecutive months sale:

Rs. (34009+ x)

Step-2: Using the average formula 1 As we know that, sum of values 

Average=sum of values / number of values….(1)

Average of six months sale is Number of values = Rs. 6500.

Number of values= 6

Now, substituting known values in eq we get,

6500=34009+x/6

6 x 6500 = 34009 + x

39000= 34009 + x 

39000- 34009 = x

⇒x=4991

Therefore, Rs.

4991 sale must he have in the sixth months.

Hence, option (C) Rs. 4991 is correct.

6)The average height of a class of 30 students is 1 m 50 cm. 6 new students increase the average height to 1 m 55 cm. Determine the average height of the 6 new students.

A) 1m 65 cm

C) 1 m 85 cm

B) 1 m 80 cm

D) 1 m 60 cm

Ans - 

Ratio of old to new students = 30: 6 = 5:1

Total height of 5 students = 5 x 150 = 750 cm

Total height of 6 students = 6 × 155 = 930 cm

average height of new students = 930-750= 180 cm

= 1 m 80 cm

7)The sum of three consecutive odd numbers is 165. What is the sum of the largest number and twice the smallest number?

A) 163

B) 175

C) 169

D) 178

Ans-

Let the numbers be x, x + 2 and x + 4

According to question -

x+(x+2)+(x+4)= 165

→ 3x+6=165

→ 3x = 159

⇒ x = 53

Smallest number = x = 53

Largest number = x + 4 = 57

The sum of the largest number and twice the smallest number = 57 + 2 × 53=57 + 106

= 163

8) Find the mean of squares of the first 10 natural numbers.

A) 38.5

B) 39.5

C) 39

D) 40

Ans- 

Sum of squares of first n natural Number = [n (n + 1) (2n + 1)]/6

Calculation:

Sum of squares of first n natural Number = [10(10+ 1)(2 × 10+ 1)]/6 = 385

Average of squares of first 10 natural numbers = sum of squares/10 385/10

Average of squares of first 10 natural numbers = 38.5

=The average of squares of first 10 natural numbers is 38.5

9) Find the average of squares of the first 11 consecutive even numbers.

A) 185

C) 186

B) 184

D) 183

Ans- 

Formula:

2*(n+1)*(2n+1)/3

Let n = 11.

2*(11+1)*(2 (11)+1)/3

2*(12)*(23)/3

= 184.

10)What is the average of squares of consecutive odd numbers between 1

and 13?

A)53

B) 64

C)69

D) 57

Ans- 

The consecutive odd numbers from 1 to 13=3,5,7,9,11

Thus required average =

3² +5² + 7² +9² + 11²/5=

9+25+49+81+121/5=

285/5= 57