Q14 of 79 Page 25

The mean of marks scored by 100 students was found to be 40. Later on it was discovered that a score of 53 was misread as 83. Find the correct mean.

Mean marks of 100 students = 40

Sum of marks of 100 students = 100 * 40


= 4000


Correct value = 53


Incorrect value = 83


Correct sum = 4000 – 83 + 53


= 3970


Therefore, correct mean =


= 39.7


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Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by the Meteorological Department are given below:

9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9


(i) Find the mean


(ii) Verify that = 0

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Explain, by taking a suitable example, how the arithmetic mean alters by (i) adding a constant k to each term, (ii) subtracting a constant k from each them, (iii) multiplying each term by a constant k and (iv) dividing each term by a non-zero constant k.

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The traffic police recorded the speed (in km/h) of 10 motorists as 47, 53, 49, 60, 39, 42, 55, 57, 52, 48. Later on an error in recording instrument was found. Find the correct overage speed of the motorists if the instrument recorded 5 km/hr. less in each case.

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The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded number.