
The mean of the numbers a, b, 8, 5, 10, is 6 and the variance is 6.80. The which one of the following gives possible values of a and b?
A)
\[a=0,b=7\] done
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B)
\[a=5,b=2\] done
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C)
\[a=1,b=6\] done
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D)
\[a=3,b=4\] done
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Suppose a population A has 100 observations \[101,102,.....,200\] and another population B has 100 observations 151, 152 ???? 250. If \[{{V}_{A}}\,\,and\,\,{{V}_{B}}\] represent the variances of the two populations, respectively then \[\frac{{{V}_{A}}}{{{V}_{B}}}\] is
A)
1 done
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B)
\[\frac{9}{4}\] done
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C)
\[\frac{4}{9}\] done
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D)
\[\frac{2}{3}\] done
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The mean of n times is \[\overline{x}\]. If the first terms is increased by 1, second by 2 and so on, then new mean is
A)
\[\bar{x}+n\] done
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B)
\[\bar{x}+\frac{n}{2}\] done
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C)
\[\bar{x}+\frac{n+1}{2}\] done
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D)
None of these done
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The mean weight per student in a group of seven students is 55 kg. if the individual weights of six students are 52, 58, 55, 53, 56 and 54, then the weight of the seventh student is
A)
55 kg done
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B)
60 kg done
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C)
57 kg done
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D)
50 kg done
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The scores of 15 students in an examination were recorded as 10, 5, 8, 16, 18, 20, 8, 10, 16, 20, 18, 11, 16, 14 and 12. After calculating the mean, median and mode, an error is found. One of the values is wrongly written as 16 instead of 18. Which of the following measures of central tendency will change?
A)
Mean and median done
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B)
Median and mode done
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C)
Mode only done
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D)
Mean and mode done
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For the data 3, 5, 1, 6, 5, 9, 2, 8, 6 the mean, median and mode are x, y, and z respectively. Which one of the following is correct?
A)
\[x=y\ne z\] done
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B)
\[x\ne y=z\] done
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C)
\[x\ne y\ne z\] done
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D)
\[x=y=z\] done
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If the standard deviation of the observations \[5,4,3,2,1,0,1,2,3,4,5\] is \[\sqrt{10}\]. The standard deviation of observations \[15,16,17,18,19,20,21,22,23,24,25\] will be
A)
\[\sqrt{10}+20\] done
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B)
\[\sqrt{10}+10\] done
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C)
\[\sqrt{10}\] done
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D)
None of these done
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If mean of the n observations \[{{x}_{1}},{{x}_{2}},{{x}_{3}},...{{x}_{n}}\] be \[\bar{x},\] then the mean of n observations \[2{{x}_{1}}+3,\,\,2{{x}_{2}}+3,\,\,2{{x}_{3}}+3,...,2{{x}_{n}}+3\] is
A)
\[3\bar{x}+2\] done
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B)
\[2\bar{x}+3\] done
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C)
\[\bar{x}+3\] done
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D)
\[2\bar{x}\] done
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If the mean deviation of the numbers \[1,\,\,1+d,\] \[1+2d,...1+100d\] from their mean is 255, then d is equal to:
A)
20.0 done
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B)
10.1 done
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C)
20.2 done
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D)
10.0 done
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The variance of the following distribution is
\[{{x}_{i}}\]  2  3  11 
\[f({{x}_{i}})\]  \[\frac{1}{3}\]  \[\frac{1}{2}\]  \[\frac{1}{6}\] 
A)
10 done
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B)
16 done
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C)
8 done
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D)
7.5 done
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A school has four sections of chemistry in class XII having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the four sections, the overall average of marks per students is
A)
53 done
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B)
45 done
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C)
55.3 done
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D)
52.25 done
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In a study of two groups, the following results were obtained:

Group Group 

A 
B 
Sample Size 
20 
25 
Sample mean 
22 
23 
Sample standard Deviation 
10 
12 
Which of the following statements is correct?
A)
Group A is less variable then Group B because Group A's standard deviation is smaller. done
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B)
Group A is less variable then Group B because Group A's sample size is smaller. done
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C)
Group A is less variable then group B because Group A's sample mean is smaller. done
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D)
Group A is less variable then group B because Group A's coefficient of variation is smaller. done
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The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
A)
28 done
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B)
30 done
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C)
35 done
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D)
38 done
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If the arithmetic mean of the numbers \[{{x}_{1}},{{x}_{2}},{{x}_{3}},...{{x}_{n}}\] is \[\bar{x}\]. Then the arithmetic mean of numbers \[a{{x}_{1}}+b,a{{x}_{2}}+b,a{{x}_{3}}+b,...a{{x}_{n}}+b,\] Where a, b are two constants would be
A)
\[\bar{x}\] done
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B)
\[na\bar{x}+nb\] done
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C)
\[a\bar{x}\] done
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D)
\[a\bar{x}+b\] done
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In an experiment with 15 observations on X, the following results were available \[\Sigma {{x}^{2}}=2830,\] \[\Sigma x=170.\] On observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is
A)
78.00 done
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B)
\[188.66\] done
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C)
\[177.33\] done
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D)
\[8.33\] done
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The average of n numbers \[{{x}_{1}},{{x}_{2}},{{x}_{3}},...{{x}_{n}}\] is M. If \[{{x}_{n}}\] is replaced by \[x',\] then new average is
A)
\[M{{x}_{n}}+x'\] done
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B)
\[\frac{nM{{x}_{n}}+x'}{n}\] done
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C)
\[\frac{(n1)M+x'}{n}\] done
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D)
\[\frac{M{{x}_{n}}+x'}{n}\] done
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If the mean of the numbers \[27+x,31+x,89+x,107+x,156+x\] is 82, then the mean of \[130+x\], \[126+x,\,\,68+x,\,\,50+x,\,\,1+x\]
A)
75 done
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B)
157 done
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C)
82 done
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D)
80 done
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The standard deviation of \[9,\,\,16,\,\,23,\,\,30,\,\,37,\,\,44,\,\,51\] is
A)
7 done
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B)
9 done
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C)
12 done
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D)
14 done
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For 10 observations on price (x) and supply (y), the following data was obtained: \[\sum{x=130,\sum{y=220,}}\] \[\sum{{{x}^{2}}=2288,\sum{{{y}^{2}}=5506}}\] and \[\sum{xy=3467}\] What is line of regression of y on x?
A)
\[y=0.91x+8.74\] done
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B)
\[y=1.02x+8.74\] done
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C)
\[y=1.02x7.02\] done
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D)
\[y=0.91x7.02\] done
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Mean of the numbers \[1,2,3,...,n\] with respective weights \[{{1}^{2}}+1,\,\,{{2}^{2}}+2,\,\,{{3}^{3}}+3,\,\,...{{n}^{2}}+n\] is
A)
\[\frac{3n(n+1)}{2(2n+1)}\] done
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B)
\[\frac{2n+1}{3}\] done
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C)
\[\frac{3n+1}{4}\] done
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D)
\[\frac{3n+1}{2}\] done
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The mean and S.D of the marks of 200 candidates were found to be 40 and 15 respectively. Latter, it was discovered that a score of 40 was wrongly read as 50. The correct mean and S. D respectively are
A)
14.98, 39.95 done
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B)
39.95, 14.98 done
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C)
39.95, 224.5 done
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D)
None of these done
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The mean income of a group of 50 persons was calculated as Rs. 169. Later it was discovered that one figure was wrongly taken as 134 instead of correct value 143. The correct mean should be (in Rs.)
A)
168 done
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B)
169 done
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C)
168.92 done
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D)
169.18 done
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The mean and S.D. of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that a score of 40 was wrongly read as 50. The correct mean and S.D. respectively are
A)
\[14.98,39.95\] done
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B)
\[39.95,14.98\] done
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C)
\[39.95,224.5\] done
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D)
None of these done
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Let \[{{x}_{1}},{{x}_{2}},...{{x}_{n}}\] be n observations such that \[\sum{x_{i}^{2}=400}\] and \[\sum{{{x}_{i}}=80.}\] Then the possible value of n among the following is
A)
15 done
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B)
18 done
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C)
9 done
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D)
12 done
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The mean of a set of observation is \[\bar{x}.\]if each observation is divided by \[\alpha ,a\ne 0\] and then is increased by 10, then the mean of the new set is
A)
\[\frac{{\bar{x}}}{a}\] done
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B)
\[\frac{\bar{x}+10}{a}\] done
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C)
\[\frac{\bar{x}+10a}{a}\] done
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D)
\[a\bar{x}+10\] done
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The mean of the series \[{{x}_{1}},{{x}_{2}},...{{x}_{n}}\] is \[\bar{X}\]. If \[{{x}_{2}}\] is replaced by \[\lambda ,\] then what is the new mean?
A)
\[\bar{X}{{x}_{2}}+\lambda \] done
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B)
\[\frac{\bar{X}{{x}_{2}}\lambda }{n}\] done
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C)
\[\frac{\bar{X}{{x}_{2}}+\lambda }{n}\] done
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D)
\[\frac{n\bar{X}{{x}_{2}}+\lambda }{n}\] done
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A fair die is tossed 180 times, the standard deviation of the number of sixes equal to
A)
\[\sqrt{30}\] done
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B)
5 done
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C)
25 done
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D)
\[\sqrt{90}\] done
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The mean mark in statistics of 100 students in a class was 72. The mean mark of boys was 75. While their number was 70. The mean mark of girls in the class was
A)
65 done
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B)
60 done
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C)
66 done
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D)
62 done
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For a series the value of mean deviation is 15. The most likely value of its quartile deviation is
A)
12.5 done
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B)
11.6 done
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C)
13 done
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D)
9.7 done
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The mean deviation from the mean of the A.P.\[a,a+d,a+2d,...a,a+2nd\] is
A)
\[n(n+1)d\] done
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B)
\[\frac{n(n+1)d}{2n+1}\] done
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C)
\[\frac{n(n+1)d}{2n}\] done
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D)
\[\frac{n(n1)d}{2n+1}\] done
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If the combined mean of two groups is \[\frac{40}{3}\] and if the mean of one group with 10 observations is 15, then the mean of the other group with 8 observation is equal to
A)
\[\frac{46}{3}\] done
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B)
\[\frac{35}{4}\] done
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C)
\[\frac{45}{4}\] done
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D)
\[\frac{41}{4}\] done
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Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is
A)
48 done
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B)
\[82\frac{1}{2}\] done
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C)
\[50\] done
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D)
\[80\] done
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The 'less than' ogive curve and the 'more than' ogive curve intersect at
A)
Median done
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B)
Mode done
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C)
Arithmetic done
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D)
None of these done
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An aeroplane flies around a squares, the sides of which measure 100 miles each. The aeroplane covers at speed of 100 m/h the first side, at 200 m/h the second side. At 300 m/h the third side and 400 m/h the fourth side. The average speed of the aeroplane around the square is
A)
900 m/h done
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B)
195 m/h done
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C)
192 m/h done
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D)
200 m/h done
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The first of two samples has 100 items with mean 15 and SD 3. If the whole group has 250 items with mean 15.6 and \[SD=\sqrt{13.44}\] the SD of the second group is
A)
5 done
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B)
4 done
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C)
6 done
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D)
3.52 done
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In a test of statistics marks were awarded out of 40. The average of 15 students was 38. Later it was decided to give marks out of 50. The new average marks will be
A)
40 done
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B)
47.5 done
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C)
95 done
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D)
41.5 done
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If \[\sum\nolimits_{i=1}^{9}{({{x}_{i}}5)=9}\] and \[\sum\nolimits_{i=1}^{9}{{{({{x}_{i}}5)}^{2}}=45,}\] then the standard deviation of the 9 items \[{{x}_{1}},{{x}_{2}},...{{x}_{9}}\] is
A)
9 done
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B)
4 done
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C)
3 done
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D)
2 done
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Variance of the numbers \[3,7,10,18,22\] is equal to
A)
12 done
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B)
6.4 done
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C)
\[\sqrt{49.2}\] done
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D)
49.2 done
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The marks obtained by 60 students in a certain test are given below:
Marks  No. of students  Marks  No. of students 
1020  2  6070  12 
2030  3  7080  14 
3040  4  8090  10 
4050  5  90100  4 
5060  6   
Mean, median and mode of the above data are respectively
A)
\[64.33,68.33,76.33\] done
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B)
\[60,70,80\] done
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C)
\[66.11,71.11,79.11\] done
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D)
None of these done
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The variance of 20 observations is 5. If each observation is multiplied by 2, then what is the new variance of the resulting observations?
A)
5 done
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B)
10 done
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C)
20 done
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D)
40 done
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The mean of 20 observations is 15. On checking, it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is
A)
15 done
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B)
15.15 done
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C)
15.35 done
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D)
16 done
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Let r be the range and \[{{S}^{2}}=\frac{1}{n1}\sum\limits_{i=1}^{n}{{{({{x}_{i}}\bar{x})}^{2}}}\] be the S.D. of a set of observations \[{{x}_{1}},{{x}_{2}},...{{x}_{n}},\] then
A)
\[S\le r\sqrt{\frac{n}{n1}}\] done
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B)
\[S=r\sqrt{\frac{n}{n1}}\] done
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C)
\[S\ge r\sqrt{\frac{n}{n1}}\] done
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D)
None of these done
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In a series of \[2n\]observations, half of them equals \['a'\] and remaining equals '__a'. If S.D. is 2, then \[\left a \right\] equals
A)
\[\frac{1}{n}\] done
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B)
\[\sqrt{2}\] done
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C)
\[2\] done
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D)
\[\frac{\sqrt{2}}{n}\] done
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Consider any set of observations \[{{x}_{1}},{{x}_{2}},{{x}_{3,...}}{{x}_{101}};\] it being given that \[{{x}_{1}}<{{x}_{2}}<{{x}_{3}}<...<{{x}_{100}}<{{x}_{101}};\] then the mean deviation of this set of observations about a point k is minimum when k equals
A)
\[{{x}_{1}}\] done
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B)
\[{{x}_{51}}\] done
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C)
\[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\] done
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D)
\[{{x}_{50}}\] done
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The mean of five observations is 4 and their variance is \[5\cdot 2\]. If three of these observations are 2, 4 and 6, then the other two observations are
A)
3 and 6 done
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B)
2 and 6 done
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C)
5 and 8 done
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D)
1 and 7 done
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The mean and SD of 63 children on an arithmetic test are respectively 27, 6 and 7.1. to them are added a new group of 26 who had less training and whose mean is 19.2 and SD. 6.2 The values of the combined group differ from the original as to (i) the mean and (ii) the SD is
A)
25.1, 7.8 done
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B)
2.3, 0.8 done
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C)
1.5, 0.9 done
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D)
None of these done
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The average marks obtained by the students in a class are 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?
A)
15 done
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B)
17 done
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C)
18 done
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D)
20 done
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The variance of first 50 even natural numbers is
A)
437 done
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B)
\[\frac{437}{4}\] done
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C)
\[\frac{833}{4}\] done
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D)
\[833\] done
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Given (i) 85 observations which are not shortest and (ii) 150 observations which are sorted and arranged in an increasing order. The median values of (i) & (ii) respectively can be found as
A)
(i) 43rd observation (ii) A.M. of 75th and 76th observation done
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B)
(i) 43rd observation (ii) 76th observation done
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C)
(i) cannot be found (ii) cannot be found done
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D)
None of these done
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Consider the frequency distribution of the given numbers.
Value  1  2  3  4 
Frequency  5  4  6  f 
If the mean is known to be 3, then the value of f is
A)
3 done
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B)
7 done
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C)
10 done
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D)
14 done
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In a binomial distribution, the mean is 4 and the variance is. What is the mode?
A)
6 done
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B)
5 done
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C)
4 done
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D)
3 done
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If the mean of few observations is 40 and standard deviation is 8, then what is the coefficient of variation?
A)
1% done
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B)
10% done
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C)
20% done
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D)
30% done
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An incomplete frequency distribution is given below
Variate  Frequency 
1020 2030 3040 4050 5060 6070 7080  12 30 ? 65 45 25 18 
Total  229 
Median value is 46, the missing frequency is
A)
33.5 done
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B)
35 done
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C)
34 done
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D)
26 done
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In the following frequency distribution. Class limits of some of the class intervals and midvale of a class are missing. However, the mean of the distribution is known to be 46.5.
Class intervals  Midvalues  Frequency 
\[{{x}_{1}}{{x}_{2}}\]  15  10 
\[{{x}_{2}}{{x}_{3}}\]  30  40 
\[{{x}_{3}}{{x}_{4}}\]  M  30 
\[{{x}_{4}}{{x}_{5}}\]  75  10 
\[{{x}_{5}}100\]  90  10 
The values of \[{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}},{{x}_{5}}\] respectively will be
A)
\[(0,20,40,60,80)\] done
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B)
\[(40,50,60,70,80)\] done
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C)
\[(10,20,40,70,80)\] done
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D)
\[(0,19.5,39.5,69.5,80)\] done
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Let \[\bar{x}\] be the mean of n observations \[{{x}_{1}},{{x}_{2}},...{{x}_{n}},\]if \[(ab)\] is added to each observation, then what is the mean of new set of observations?
A)
0 done
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B)
\[\bar{x}\] done
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C)
\[\bar{x}(ab)\] done
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D)
\[\bar{x}+(ab)\] done
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Students of two schools appeared for a common test carrying 100 marks. The arithmetic means of their marks of school I and II are 82 and 86 respectively. If the number of students of school II is 1.5 times the number of students of school I, what is the arithmetic mean of the marks of all the students of both are schools?
A)
84.0 done
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B)
84.2 done
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C)
84.4 done
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D)
This cannot be calculated with the given data done
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The range of a random variable x is \[\{1,2,3,...\}.\] If \[P(x=r)=\frac{1}{{{2}^{r}}}\], then the mean of the distribution is
A)
8 done
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B)
16 done
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C)
1 done
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D)
2 done
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One set containing five members has mean 8, variance 18 and the second set containing three members has mean 8 and variance 24. The variance of combined set of numbers is
A)
24 done
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B)
20.25 done
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C)
22.25 done
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D)
None of these done
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The arithmetic mean of numbers a, b, c, d, e, is M. What is the value of \[(aM)+(bM)+(cM)+(dM)+(eM)?\]
A)
M done
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B)
\[a+b+c+d+e\] done
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C)
0 done
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D)
5 M done
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The mean of 13 observations is 14. If the mean of the first 7 observations is 12. And that of the least 7 observations is 16, what is the value of the 7th observations?
A)
12 done
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B)
13 done
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C)
14 done
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D)
15 done
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