Average
- The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next inning so as to increase his average of runs by 4 ?
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Let the batsman make p runs.
Total runs in 10 innings = 10 × 32 = 320∴ 320 + p = 32 + 4 11
⇒ 320 + p = 36 × 11
⇒ p = 396 – 320 = 76
Second method to solve this question with the help of given formula :
Here, T = 32, N = 11, t = 4
Correct Option: A
Let the batsman make p runs.
Total runs in 10 innings = 10 × 32 = 320∴ 320 + p = 32 + 4 11
⇒ 320 + p = 36 × 11
⇒ p = 396 – 320 = 76
Second method to solve this question with the help of given formula :
Here, T = 32, N = 11, t = 4
Required Run = T + Nt [Here N is taken as (n + 1)]
Required Run = 32 + 11 × 4
Required Run = 32 + 44 = 76
- The average of 9 observations was found to be 35. Later on, it was detected that an observation 81 was misread as 18. The correct average of the observations is :
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Given that , The average of 9 observations = 35
Later on, it was detected that an observation 81 was misread as 18 .
Correct sum of 9 observations = 9 × 35 – 18 + 81
Correct sum of 9 observations = 315 + 63 = 378Correct Option: B
Given that , The average of 9 observations = 35
Later on, it was detected that an observation 81 was misread as 18 .
Correct sum of 9 observations = 9 × 35 – 18 + 81
Correct sum of 9 observations = 315 + 63 = 378
∴ Required correct average = 378 ÷ 9 = 42
- A student, by mistake, wrote 64 in place of 46 as a number at the time of finding the average of 10 given numbers and got the average as 50. The correct average of the numbers is :
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Here , Average of 10 given numbers = 50
A student, by mistake, wrote 64 in place of 46 , then
Correct sum of numbers = 10 × 50 – 64 + 46
Correct sum of numbers = 500 – 18 = 482Correct Option: A
Here , Average of 10 given numbers = 50
A student, by mistake, wrote 64 in place of 46 , then
Correct sum of numbers = 10 × 50 – 64 + 46
Correct sum of numbers = 500 – 18 = 482
∴ Correct average = 482 ÷ 10 = 48.2
- The average marks obtained by a student in 6 subjects is 88. On subsequent verification it was found that the marks obtained by him in a subject was wrongly copied as 86 instead of 68. The correct average of the marks obtained by him is
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Here , The average marks obtained by a student in 6 subjects = 88
Correct sum of marks obtained by the student = 88 × 6 – 86 + 68
Correct sum of marks obtained by the student = 528 – 86 + 68 = 510
∴ Correct average = 510 ÷ 6 = 85
Second method to solve this question with the help of given formula :
Here, n = 6, m = 88 a = 68, b = 86Correct mean = m + (a - b) n
Correct Option: B
Here , The average marks obtained by a student in 6 subjects = 88
Correct sum of marks obtained by the student = 88 × 6 – 86 + 68
Correct sum of marks obtained by the student = 528 – 86 + 68 = 510
∴ Correct average = 510 ÷ 6 = 85
Second method to solve this question with the help of given formula :
Here, n = 6, m = 88 a = 68, b = 86Correct mean = m + (a - b) n Correct mean = 88 + (68 - 86) 6 Correct mean = 88 - 18 6
Correct mean = 85
- The average of 20 numbers is calculated as 35. It is dicovered later, that while calculating the average, one number, namely 85, was read as 45. The correct average is
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According to question ,
Correct sum of 20 numbers = 20 × 35 – 45 + 85
Correct sum of 20 numbers = 700 + 40 = 740∴ Correct average = 740 = 37 20
Second method to solve this question with the help of given formula :
Here, n = 20, m = 35 , a = 85, b = 45
Correct Option: B
According to question ,
Correct sum of 20 numbers = 20 × 35 – 45 + 85
Correct sum of 20 numbers = 700 + 40 = 740∴ Correct average = 740 = 37 20
Second method to solve this question with the help of given formula :
Here, n = 20, m = 35 , a = 85, b = 45Correct mean = m + (a - b) n Correct mean = 35 + (85 - 45) = 35 + 2 = 37 20
