RD Chapter 24 Measures of Central Tendency Ex 24.1 Solutions
Question - 11 : - 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.
Answer - 11 : - Let x1, x2, x3, x4, x5 are five numbers whose mean is 
Hence we see that in each case, the mean is changed.
Question - 12 : - The mean of marks scored by 100 students was found to be 40. Later on its was discovered that a score of 53 was misread as 83. Find the correct mean.
Answer - 12 : -
Mean score of 100 students = 40
∴Total = 100 x 40 = 4000
Difference in one score by mistake = 83 – 53 = 30
Actual total scores = 4000 – 300 = 3970
Actual mean = 3970/100 = 39.70 = 39.7
Question - 13 : - The traffic police recorded the speed (in km/hr) 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 average speed of the motorists if the instrument recorded 5 km/hr less in each case.
Answer - 13 : -
Speed of 10 motorist as recorded = 47, 53, 49, 60, 39, 42, 55, 57, 52, 48
Total of speed of 10 motorists = 47 + 53 + 49 + 60 + 39 + 42 + 55 +57 + 52 + 48 = 502
Question - 14 : - The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded number.
Answer - 14 : -
Mean of 5 numbers = 27
Total = 27 x 5 = 135
By excluded one number, then mean of remaining 4 numbers = 25
Total = 4 x 25 = 100
Excluded number = 135 – 100 = 35
Question - 15 : - The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.
Answer - 15 : -
Mean weight of 7 students = 55 kg
Total weight of 7 students = 55 x 7 kg = 385 kg
Total weights of 6 students among them = 52 + 54 + 55 + 53 + 56 + 54 = 324 kg
Weight of 7th student = 385 – 324 = 61 kg
Question - 16 : - The mean weight of 8 numbers is 15. If each number is multiplied by 2, what will be the new mean?
Answer - 16 : -
Weight of 8 numbers =15
By multiplying each number by 2, then the average will be = 15 x 2 = 30
New average = 30
Question - 17 : - The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.
Answer - 17 : -
Mean of 5 numbers = 18
Total = 18 x 5 = 90
By excluding one number, the mean of remaining 5 – 1=4 numbers = 16
Total = 16 x 4 = 64
Excluded number = 90 – 64 = 26
Question - 18 : - The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.
Answer - 18 : -
Mean of 200 items = 50
Total = 50 x 200 = 10000
The number were misread as 92 instead of 192 and 8 instead of 88
Difference = 192 – 92 + 88 – 8 = 180
New total = 10000 + 180 = 10180
and new mean = 10180/200 = 50.9
Question - 19 : - If M is the mean of x1, x2, xr3, x4, x5 and x6, prove that
(x1 – M) + (x2 – M) + (x3 – M) + (x4 – M) + (x5 – M) + (x6 – M) = 0.
Answer - 19 : - ∵ M is the mean of x,, x2, x3, x4, x5, x6
Question - 20 : - 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 
Answer - 20 : -
Duration of sun shine for 10 days (in hours)
= 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9