Mean marks obtained by 10 students are estimated to be 40. Later on it is found that one value was read as 14 instead of 24. Find the corrected mean.
a) 26
b) 27
c) 28
d) 29
Answers
Answer:
The mean of 10 observations was found to be 28. Later, it was discovered that one observation 14 was misread as 24. Find the correct mean? (A) 25 (B) 26 (C) 27 (D) 29
Mean =sum of observation ÷no. Of observation
According to first statement
Sum=280
As instead of 14,24 was misread,so we have to subtract 24 from 280
280-24=256
Then,we add correct observation i.e 14 in 256
256+14=270
Now , correct mean=270÷10=27
So, correct mean is 27
Mean of 10 observations = 28
Total of 10 observations = 280 [incorrect total]
Correct total = 280 + 14 - 24 = 280 - 10 = 270
The correct mean = 270/10 = 27
When we talk about the “mean” or the “arithmetic mean” of two or more quantities, we are actually talking about the average of those quantities.
The average of two or more quantities is found by simply adding the quantities together and then dividing this sum by the number of quantities. In this case, we have the following mean or average:
mean (average) = (The sum S of the observations)/(the number n of observations)
mean = S/n
28 = S/10
28(10) = 10(S/10)
280 = S
Since equality is symmetric, i.e., if a = b, then b = a,
What is the correct mean if the mean of 50 observations was 80 but it was later discovered that observation 19 was recorded by mistake as 91?
The mean of 9 observations is 1269 the mean of the first 5 observations is 144.6 and the mean of the last 5 observations is 13 9.4, what is the value of 4 observation?
The mean of 20 observations is 5.1. By mistake, one observation is taken as+7 instead of -7. What is the correct mean?
The sum of all of the observations originally was 10*28=280. This was 10 too high, so the correct sum is 280-10=270. Thus the mean is 270/10 = 27. (C)
Correction = (-24 + 14) / 10 = -1
Corrected mean = 28 - 1 = 27 (Answer)
Step-by-step explanation:
=> Mean of 10 observations = 28
=> Sum of 10 observations = 28*10
=> Sum of 10 observations =280
• since 14 was misread as 24
Then, sum of new observations = [280- (wrong observation)+(correct observation)]
= 280–24+14
= 280-10= 270
The correct mean = some of new observation/total number of observations
Correct mean= 270/10=27
Hence, the correct mean is 27 (C).
27
x1+…….+24+……x10=28X10 (wrong sum)
x1+…….+14+……x10=28X10-(24–14) (correct sum)
correct mean=(28X10)/10 -10/10=28–1=27
Answer:
41
Explanation:
sum of total observation = 10 * 40
= 400
sum of correct observations = 400 - 14 + 24
= 410
mean = sum of observations / no of observations
= 410 / 10
= 41