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DATA HANDLING

300097 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Mode is the most frequent value.
Reason: The value which occurs the maximum number of times in the dataset or which has the highest frequency is the mode of the dataset.

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

DATA HANDLING

300098 The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

1 0

2 1

3 10

4 19

Explanation:

19
Let the 20 numbers be a $_{\1}$ ?, a $_{\1}$ ?, .... ,a $_{\1}$
Given that average of 20 numbers is zero.
$∴ \frac{a_{1} + a_{2} + . . . + a_{20}}{20}$
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ ?=0
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ = -a $_{\1}$
$∴$ at the most 19 numbers can be greater than zero.

DATA HANDLING

300099 If the average marks of three batches of 55, 60 and 45, students respectively is 50, 55 and 60, then what are the average marks of all the students?

1 43.5879

2 65.7824

3 54.6875

4 34.2278

Explanation:

54.6875
Total marks of first batch = 55 × 50 = 2750
total marks of second batch = 60 × 55 = 3300
total marks of third batch = 45 × 60 = 2700
total number of students in three batch = 55 + 60 + 45 = 160
$∴$ average marks of all the students $= \frac{2750 + 3300 + 2700}{160} = \frac{8750}{160}$
= 54.6875

DATA HANDLING

300100 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The marks of 20 students in a test were as follows: 5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. The mean is 13.
Reason: $Mean = \frac{sum of marks}{number of students} = \frac{260}{20} = 13.$

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

DATA HANDLING

300097 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Mode is the most frequent value.
Reason: The value which occurs the maximum number of times in the dataset or which has the highest frequency is the mode of the dataset.

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

DATA HANDLING

300098 The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

1 0

2 1

3 10

4 19

Explanation:

19
Let the 20 numbers be a $_{\1}$ ?, a $_{\1}$ ?, .... ,a $_{\1}$
Given that average of 20 numbers is zero.
$∴ \frac{a_{1} + a_{2} + . . . + a_{20}}{20}$
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ ?=0
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ = -a $_{\1}$
$∴$ at the most 19 numbers can be greater than zero.

DATA HANDLING

300099 If the average marks of three batches of 55, 60 and 45, students respectively is 50, 55 and 60, then what are the average marks of all the students?

1 43.5879

2 65.7824

3 54.6875

4 34.2278

Explanation:

54.6875
Total marks of first batch = 55 × 50 = 2750
total marks of second batch = 60 × 55 = 3300
total marks of third batch = 45 × 60 = 2700
total number of students in three batch = 55 + 60 + 45 = 160
$∴$ average marks of all the students $= \frac{2750 + 3300 + 2700}{160} = \frac{8750}{160}$
= 54.6875

DATA HANDLING

300100 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The marks of 20 students in a test were as follows: 5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. The mean is 13.
Reason: $Mean = \frac{sum of marks}{number of students} = \frac{260}{20} = 13.$

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

DATA HANDLING

300097 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Mode is the most frequent value.
Reason: The value which occurs the maximum number of times in the dataset or which has the highest frequency is the mode of the dataset.

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

DATA HANDLING

300098 The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

1 0

2 1

3 10

4 19

Explanation:

19
Let the 20 numbers be a $_{\1}$ ?, a $_{\1}$ ?, .... ,a $_{\1}$
Given that average of 20 numbers is zero.
$∴ \frac{a_{1} + a_{2} + . . . + a_{20}}{20}$
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ ?=0
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ = -a $_{\1}$
$∴$ at the most 19 numbers can be greater than zero.

DATA HANDLING

300099 If the average marks of three batches of 55, 60 and 45, students respectively is 50, 55 and 60, then what are the average marks of all the students?

1 43.5879

2 65.7824

3 54.6875

4 34.2278

Explanation:

54.6875
Total marks of first batch = 55 × 50 = 2750
total marks of second batch = 60 × 55 = 3300
total marks of third batch = 45 × 60 = 2700
total number of students in three batch = 55 + 60 + 45 = 160
$∴$ average marks of all the students $= \frac{2750 + 3300 + 2700}{160} = \frac{8750}{160}$
= 54.6875

DATA HANDLING

300100 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The marks of 20 students in a test were as follows: 5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. The mean is 13.
Reason: $Mean = \frac{sum of marks}{number of students} = \frac{260}{20} = 13.$

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

DATA HANDLING

300097 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Mode is the most frequent value.
Reason: The value which occurs the maximum number of times in the dataset or which has the highest frequency is the mode of the dataset.

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

DATA HANDLING

300098 The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

1 0

2 1

3 10

4 19

Explanation:

19
Let the 20 numbers be a $_{\1}$ ?, a $_{\1}$ ?, .... ,a $_{\1}$
Given that average of 20 numbers is zero.
$∴ \frac{a_{1} + a_{2} + . . . + a_{20}}{20}$
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ ?=0
a $_{\1}$ ? + a $_{\1}$ ? + ... +a $_{\1}$ = -a $_{\1}$
$∴$ at the most 19 numbers can be greater than zero.

DATA HANDLING

300099 If the average marks of three batches of 55, 60 and 45, students respectively is 50, 55 and 60, then what are the average marks of all the students?

1 43.5879

2 65.7824

3 54.6875

4 34.2278

Explanation:

54.6875
Total marks of first batch = 55 × 50 = 2750
total marks of second batch = 60 × 55 = 3300
total marks of third batch = 45 × 60 = 2700
total number of students in three batch = 55 + 60 + 45 = 160
$∴$ average marks of all the students $= \frac{2750 + 3300 + 2700}{160} = \frac{8750}{160}$
= 54.6875

DATA HANDLING

300100 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The marks of 20 students in a test were as follows: 5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. The mean is 13.
Reason: $Mean = \frac{sum of marks}{number of students} = \frac{260}{20} = 13.$

1 Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

2 Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

3 Assertion is true but the reason is false.

4 Both assertion and reason are false.

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