Statistics Test

Result

Statistics Test - 2

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Question 1
1 / -0

In a class there are 40 students and their mean marks are 80. If 20 students who have mean marks equal to 15, leave the class and after that 15 more student who have mean marks 30, admit in the class, find the new mean (approximate).

A
95.71

B
105.71

C
125.52

D
150.36

Solution

Mean marks of 40 students = 80
Sum of marks of 40 students = 80 × 40 = 3200
Now, mean marks of 20 students who leave = 15
Sum of marks of 20 students who leave = 15 × 20 = 300
Now, mean marks of 15 students who take admission = 30
Sum of marks of 15 students who take admission = 15 × 30 = 450
Total students = 40 – 20 + 15 = 35
Sum of marks of 35 students = 3200 – 300 + 450 = 3350
New mean = 3350/35
= 95.71 (approximately)
Question 2
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A shop-keeper made a list of the weights of the cakes (in grams) sold by him in a day, which is as follows:
200, 250, 500, 200, 500, 1000, 550, 750, 200, 1000, 950, 900, 850, 750, 650, 650, 500, 200, 350, 450, 400, 500, 550, 750, 500, 850, 950, 1000
If the intervals in the data are maintained in such a way: 1 - 200, 201 - 400, 401 - 600, 601 - 800, 801 - 1000, find the ratio of the frequency of the number of cakes sold in category 201 - 400 to 401 - 600.

A
5 : 7

B
5 : 3

C
4 : 7

D
3 : 8

Solution

Weights of the cakes sold by the shop-keeper: 200, 250, 500, 200, 500, 1000, 550, 750, 200, 1000, 950, 900, 850, 750, 650, 650, 500, 200, 350, 450, 400, 500, 550, 750, 500, 850, 950, 1000

After sorting this data we have, 200, 200, 200, 200, 250, 350, 400, 450, 500, 500, 500, 500, 500, 550, 550, 650, 650, 750, 750, 750, 850, 850, 900, 950, 950, 1000, 1000, 1000

From given data this table is formed:

Mass (in grams) frequency

1 - 200 4

201 - 400 3

401 - 600 8

601 - 800 5

801 - 1 000 8

From the above table it is clear that the ratio required = 201 - 400 : 401 - 600 = 3 : 8 = 3 : 8
Question 3
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In a departmental store on Wednesday, 15 candies, 11 chocolates, and 15 t-shirts were sold. On the same day, there was a sale of denims and jackets where the sale of denims was double the sale of jackets. If the average count of all the products sold was 16, find the number of denims and jackets sold together.

A
38

B
39

C
40

D
41

Solution

According to question, average count of all the products sold on Wednesday = 16
Number of different products available = 5
So, total goods sold = 16 × 5 = 80
Let the number of jackets sold be x.
So, the number of denims sold = 2x (given)
According to the given instructions,
15 candies + 11 chocolates + 15 t-shirts + 2x denims + x jackets = 80
So, 15 + 11 + 15 + 2x + x = 80
41 + 3x = 80
3x = 80 – 41 = 39
x = 39 ÷ 3 = 13
Number of jackets = x = 13
Number of denims = 2x = 2 × 13 = 26
So, number of denims and jackets sold together = 26 + 13 = 39
Question 4
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In a park there are 120 marbles in which red, blue and green marbles are in the ratio 5 : 4 : 3. The average weight of the blue marbles is 30 grams, that of the red marbles is 60 grams and that of the green marbles is half that of the blue marbles. Find the mean weight of all the marbles.

A
38.75 grams

B
39.75 grams

C
40.75 grams

D
41.75 grams

Solution

Total marbles = 120
Ratio of all type of marbles = Red : Blue : Green = 5 : 4 : 3
Mean weight = (60 × 5 + 30 × 4 + 15 × 3) ÷ 12
= (300 + 120 + 45) ÷ 12 = 38.75 grams