Questions on Correction Method

1. The analysis of the results of a budget survey of 150 families gave an average monthly expenditure of $ 120 on food items with a standard deviation of $ 15. .After the analysis was completed it was noted that figure recorded for one house-hold was wrongly taken as $ 15 instead of $ 105. Determine the correct value of the average expenditure and its standard deviation.(Ans.: S.D. 12.4; Correct average = 120.6)

2. For a distribution of 280 observations mean and standard deviation were found to be 54 and 3 respectively. On checking it was discovered that two observations which should correctly read as 62 and 82 had been wrongly recorded as 64 and 80 respectively. Calculate the correct values of mean and standard deviation.

(Ans.: Mean = 54 S.D.  = 3.0425)

3. For a frequency distribution of marks in statistics of 200 candidates (grouped in intervals of 0—5,: 5—10, etc.) the mean and standard deviation were found to be 40 and 15. Later, it was discovered that the ore 43 was misread as 53 in obtaining the frequency distribution. Find the corrected mean and standard deviation corresponding to the corrected quench distribution.

    [Ans.: Mean = 39.95   S.D. = 14.97]

4. The mean and standard deviation of 200 items are found to be and 20 respectively. If at the time of calculations, two items were only taken as 3 and 67 instead of 18 and 17. Find the correct mean, d standard deviation. What is the correct coefficient a of variation?

 (Ans.: Mean = 59.8 ,S.D. = 20.094)

5. (a) If the mean and standard deviation of series of 100 values are 50 and 4 respectively. Find the sum of item values and the sum of squares of items values.  (Ans.: (i) 5000   (ii) 251600)

(b) Coefficient of variation of two series are 75% and 90% and their standard deviations t5 and 18 respectively. Find their mean.(Ans.: Mean = 20 for both)

6. The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking it was found that one item 8 was incorrect. Calculate the mean and standard deviation if:

(i) The wrong item is omitted, and

(ii) It is replaced by 12.    [Ans.: (i) X 9.6, a σ  2.94 (ii) X 10.2; = 1.897]

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