Consider the following frequency distribution: x& | Average Questions & Answers

Q:

Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was :

A) Rs. 292.50	B) Rs. 297.50
C) Rs. 298	D) Rs. 298.50

Answer & Explanation Answer: A) Rs. 292.50

Explanation:

Let the average expenditure be Rs. x Then,

9x=[(8*30)+(x+20)]<=>9x =x+260 <=> x =32.50

Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50

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Q:

A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was :

A) 665	B) 657
C) 658	D) 678

Answer & Explanation Answer: A) 665

Explanation:

Let the total score be x.

(x + 92 - 85) / 8 = 84.

So, x + 7 = 672 => x = 665.

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Q:

The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is :

A) 35	B) 36.5
C) 40	D) 42

Answer & Explanation Answer: B) 36.5

Explanation:

Correct Sum = (36 * 50 + 48 - 23) = 1825.

Correct mean = = 1825/50 = 36.5

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Q:

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $\frac{a^{2} + b^{2} + c^{2}}{3}$ is :

A) M	B) 3 M^2
C) 2 (M/3)	D) M^2

Answer & Explanation Answer: B) 3 M^2

Explanation:

We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.

Now. ${(a + b + c)}^{2} = {(3 M)}^{2} = 9 M^{2}$ .

$< = > a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 9 M^{2}$

$a^{2} + b^{2} + c^{2} = 9 M^{2}, (a b + b c + c a = 0)$

Required mean = $(\frac{a^{2} + b^{2} + c^{2}}{3}) = \frac{9 M^{2}}{3} = 3 M^{2}$ .

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35 27518

Q:

A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?

A) 6	B) 7
C) 8	D) 9

Answer & Explanation Answer: B) 7

Explanation:

Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.

or 137 + x = 144 or x = 144 - 137 = 7.

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Q:

The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ?

A) 16,12	B) 10,16
C) 23,9	D) 8,7

Answer & Explanation Answer: B) 10,16

Explanation:

Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)]

= Rs. (120 - 94) = Rs. 26.

let the price of one book be Rs. x

Then, the price of other book = Rs. (x + 60% of x) = Rs.(x+(3/5)x) = Rs. (8/5)x

So, x+(8/5)x =26 <=> x =10

The prices of the two books are Rs. 10 and Rs. 16

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Q:

The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :

A) 6000	B) 7000
C) 8888	D) 9000

Answer & Explanation Answer: D) 9000

Explanation:

Let their prices be 3x, 5x and 7x.

Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.

Cost of cheapest item = 3x = Rs. 9000.

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Q:

The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?

A) 62 degrees	B) 64 degrees
C) 65 degrees	D) 66 degrees

Answer & Explanation Answer: B) 64 degrees

Explanation:

Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)

Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)

Subtracting (1) From (2), we get :

Temp, on 5th day - Temp on 1st day = 8 degrees.

Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.

Then, 8x - 7x = 8 or x = 8.

Temperature on the 5th day = 8x = 64 degrees.

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Consider the following frequency distribution:

x f

8 6

5 4

6 5

10 8

9 9

4 6

7 4

What is the median for the distribution?

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Consider the following frequency distribution: x f 8 6 5 4 6 5 10 8 9 9 4 6 7 4 What is the median for the distribution?

Quick Links

Consider the following frequency distribution:

x f

8 6

5 4

6 5

10 8

9 9

4 6

7 4

What is the median for the distribution?