model 1 basic average questions Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Mean of Ten observations – Mean of nine observations

Tenth observation

= 10 × 17 – 16 × 9

= 170 – 144 = 26

Aliter : Using Rule 19,

Here, N = 9, T = 16

n = 1, t = 1

10th observation

= T+ $({N/n}+1)$t

= 16+$(9/1+1) ×1$

= 16 + 10 = 26

Answer: (b)

Number of natural numbers = x

∴ Their sum = 15x

According to the question,

15x + 30 – 5 = x × 17.5

⇒ 17.5x – 15x = 25

⇒ 2.5x = 25

⇒ x = $25/2.5$ = 10

Answer: (a)

Using Rule 2,

If the given observations (x) are occuring with certain frequency (A) then,

$Average = {A_1x_1+A_2x_2+...............+A_nx_n}/{x_1+x_2+......+x_n}$

Average income of whole group

= ${4200×40+4000×35}/75$

= ${168000+140000}/75$

= $308000/75$ =Rs. 4106$2/3$

Answer: (a)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Total expenditure of the year

= Rs.(3 × 2200 + 4 × 2550 + 5 × 3120)

= Rs. (6600 + 10200 + 15600)

= Rs.32400

∴ Total income of the year

= Rs. (32400 + 1260)

= Rs.33660

∴ Average monthly income

= Rs.$33660/12$ = Rs. 2805

Answer: (c)

Average cost of a chair

=Rs. x, then

x × 12 + 6 × 750 = 7800

⇒ 12x = 7800 – 4500 = 3300

⇒ x = $3300/12$ = Rs. 275

Answer: (a)

Using Rule 18,

If in the group of N persons, a new person comes at the place of a person of ‘T’ years, so that average age, increases by ‘t’ years

Then, the age of the new person = T + N.t

If the average age decreases by ‘t’ years after entry of new person, then the age of the new person = T – N.t

Here, N = 15, T = 42, t = 1.6

Weight of new oarsman

= (42 + 15 × 1.6) kg.

= (42 + 24) kg. = 66 kg.