Q8 of 108 Page 32

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?

To Find: Find the correct mean and standard deviation.


Explanation: Here, n=100,


X =




Now,


Corrected


3990


So, The mean of correct score =



Mean = 39.9


Now, Standard variance = 5.1


Since, Variance =


Variance = 26.01


X =


26.01 =


26.01 =



Corrected -50+40


Corrected


Corrected Variance =



1625.91-1592.01


Corrected variance =34 (Approx)


Now, Corrected Standard Deviation =



Correct Deviation is 5.83


Hence, The correct Mean is 39.9 and Correct SD is 5.83


More from this chapter

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6

The mean and variance of 8 observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

 7

For a group of 200 candidates, the mean find the standard deviations of scores were found to be 40 and 15 respectively. Later on, it was discovered that the scores of 43 and 35 were misread as 34 and 53 respectively. Find the correct mean and standard deviation.

 9

The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases :

(i) If wrong item is omitted


(ii) if it is replaced by 12.

 10

The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on, it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations were omitted.