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question_answer1)
In the formula \[\overline{x}=a+\frac{\sum{{{f}_{i}}{{d}_{1}}}}{\sum{{{f}_{i}}}}\], for finding the mean of grouped data, \[{{d}_{i}}'s\] are deviation from a of
A)
Lower limits of the classes done
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B)
Upper limits of the classes done
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C)
Mid-points of the classes done
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D)
Frequencies of the class marks done
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question_answer2)
If \[{{x}_{i}}'s\] are the mid-point of the class intervals of grouped data, \[{{f}_{i}}'s\] are the corresponding frequencies and \[\overline{x}\] is the mean, then \[\sum{\left( {{f}_{i}}{{x}_{i}}-\overline{x} \right)}\] is equal to
A)
0 done
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B)
- 1 done
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C)
1 done
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D)
2 done
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question_answer3)
Consider the following frequency distribution.
Class |
Frequency |
0 - 5 |
13 |
6 - 11 |
10 |
12 - 17 |
15 |
18 - 23 |
8 |
24 - 29 |
11 |
The upper limit of the median class is
A)
17 done
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B)
17.5 done
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C)
18 done
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D)
18.5 done
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question_answer4)
Find the weighted mean of first 'n' natural numbers, whose weights are proportional to the corresponding numbers.
A)
\[\frac{2n+1}{3}\] done
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B)
\[\frac{4n+1}{3}\] done
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C)
\[\frac{{{n}^{2}}{{(n+1)}^{2}}}{2}\] done
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D)
\[\frac{(4n+1)(3n+1)}{7}\] done
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question_answer5)
What is the mean of - 7, - 5, 4, 8?
A)
1 done
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B)
Zero done
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C)
8 done
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D)
2 done
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question_answer6)
The A.M. of a set of 100 numbers is 43. If two numbers of the set, namely 65 and 35 are discarded, find the mean of the remaining observations.
A)
42.86 done
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B)
39 done
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C)
43.67 done
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D)
40 done
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question_answer7)
The A.M. of 'n' numbers of a series is X, If the sum of first (n - 1) terms is 'k', what Is the nth number?
A)
\[n\overline{X}-nk\] done
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B)
\[n\overline{X}-k\] done
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C)
\[\overline{X}-nk\] done
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D)
\[\overline{X}-k\] done
clear
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question_answer8)
If the mean of first 'n' odd natural numbers is 'n' itself what is the value of 'n'?
A)
2 done
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B)
3 done
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C)
1 done
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D)
Any natural number done
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question_answer9)
The A.M. of 'n' observations is M. If the sum of \[(n-4)\] observations is 'a', what is the mean of remaining 4 observations?
A)
\[nM+a\] done
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B)
\[\frac{nM-a}{2}\] done
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C)
\[\frac{nM+a}{2}\] done
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D)
\[\frac{nM-a}{4}\] done
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question_answer10)
The given table shows the number of packets arrange by 24 students in a day in a there classroom.
Number of Packets |
Number of Students \[({{f}_{i}})\] |
Class mark \[{{y}_{i}}\] |
\[{{d}_{i}}={{y}_{i}}-a\] |
\[{{f}_{i}}{{d}_{i}}\] |
50 - 60 |
f' |
|
|
- 60 |
60 - 70 |
f" |
|
|
|
70 - 80 |
5 |
|
|
0 |
80 - 90 |
2f' |
|
|
|
90 - 100 |
f" - 2 |
|
|
|
What is the mean number of packets arrange by students in the class?
A)
56 done
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B)
66 done
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C)
78 done
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D)
76 done
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question_answer11)
If \[{{x}_{1}},{{x}_{2}},.......,{{x}_{n}}\] are 'n' observations such that \[\sum\limits_{1}^{n}{\left( {{x}_{1}}+5 \right)=200}\] and \[\sum\limits_{1}^{n}{\left( {{x}_{1}}+9 \right)=400}\]; then find 'n'.
A)
30 done
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B)
50 done
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C)
70 done
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D)
90 done
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question_answer12)
The mean of the scores \[{{x}_{1}},{{x}_{2}},.......,{{x}_{n}}\] is x. What is the mean of the scores of \[7{{x}_{1}},7{{x}_{2}},.......,7{{x}_{6}}\]?
A)
\[x-42\] done
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B)
\[\frac{x}{7}\] done
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C)
\[~x\,\text{+}\,42\] done
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D)
\[7x\] done
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question_answer13)
The given table lists the frequency distribution of 24 observations. Some values are missing in the table.
Class Interval |
Frequency\[({{f}_{i}})\] |
Class mark \[({{x}_{i}})\] |
\[{{d}_{i}}={{x}_{i}}-a\] |
\[{{f}_{i}}{{d}_{i}}\] |
0 -50 |
\[{{f}_{1}}\] |
|
|
- 600 |
50 - 100 |
\[{{f}_{2}}\] |
|
|
|
100 - 150 |
3 |
|
|
0 |
150 - 200 |
2\[{{f}_{1}}\] |
|
|
|
200 - 250 |
2\[{{f}_{1}}\] |
|
|
|
Total |
24 |
|
|
|
What is the mean of the data set?
A)
125.5 done
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B)
131.25 done
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C)
137 done
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D)
150 done
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question_answer14)
The arithmetic mean of 1, 2, 3.................,n is
A)
\[\frac{n+1}{2}\] done
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B)
\[\frac{n}{2}+2\] done
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C)
\[\frac{n-1}{2}\] done
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D)
None of these done
clear
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question_answer15)
The mean of \[x-5y,x-3y,x-y,x+y,x+3y\] and \[x+5y\] is 22. Then, the value of x is
A)
13 done
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B)
22 done
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C)
6y done
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D)
3y done
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question_answer16)
The arithmetic mean of the squares of first 'n' natural numbers is __________.
A)
\[\frac{(n-1)(2n+1)}{6}\] done
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B)
\[\frac{n+1}{6}\] done
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C)
\[\frac{{{n}^{2}}-1}{6}\] done
clear
D)
None of these done
clear
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question_answer17)
The mean of the data \[x,x+a,x+2a,x+3a,......(2n+1\,\,terms)\]is _____.
A)
\[x+(n-1)a\] done
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B)
\[x+(n+1)a\] done
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C)
\[x+(n+2)a\] done
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D)
\[x+an\] done
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question_answer18)
The distribution below shows the number of wickets taken by bowlers in one - day cricket matches. Find the mean number of wickets by choosing a suitable method.
Number of wickets |
Number of bowlers |
20 - 60 |
7 |
60 - 100 |
5 |
100 - 150 |
16 |
150 - 250 |
12 |
250 - 350 |
2 |
350 - 450 |
3 |
A)
133.67 done
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B)
145.23 done
clear
C)
152.0 done
clear
D)
152.89 done
clear
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question_answer19)
The table below shows the daily expenditure on food of 25 households in a locality.
Daily expenditure in Rs. |
Number of households |
100 - 150 |
4 |
150 - 200 |
5 |
200 - 250 |
12 |
250 - 300 |
2 |
300 - 350 |
2 |
What is true about the mean daily expenditure on food?
A)
value of mean is 206.6 done
clear
B)
value of mean is 211 done
clear
C)
mean lies in interval (150 - 200) done
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D)
mean lies in interval (300 - 350) done
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question_answer20)
A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. (NCERT question, slightly modified)
Number of days |
Number of students |
0 - 5 |
11 |
5 - 10 |
10 |
10 - 15 |
7 |
15 - 20 |
4 |
20 - 25 |
4 |
25 - 30 |
3 |
30 - 35 |
1 |
A)
11.625 done
clear
B)
10.375 done
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C)
8.965 done
clear
D)
12.25 done
clear
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question_answer21)
Which of the following is not correct?
A)
Empirical relationship between mean, median, mode is 3 median = 2 mean + mode done
clear
B)
The above given graph shows a more than ogive done
clear
C)
First quartile \[{{Q}_{1}}=\left( \frac{n+1}{4} \right)th\] term when n is even and n is number of observations. done
clear
D)
For individual data, second quartile, \[{{Q}_{2}}=median\]. done
clear
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question_answer22)
A sequence, \[a,ax,a{{x}^{2}},......,a{{x}^{n}},\] has odd number of terms. Find its median
A)
\[ax{{n}^{-1}}\] done
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B)
\[a{{x}^{\frac{n}{2}-1}}\] done
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C)
\[a{{x}^{\frac{n}{2}}}\] done
clear
D)
\[a{{x}^{\frac{n}{2}+1}}\] done
clear
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question_answer23)
Which of the following is incorrect?
A)
\[\operatorname{var}(ax+b)={{a}^{2}}\times \operatorname{var}(x)\] done
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B)
SD does not get altered when every term is decreased by fixed amount. done
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C)
SD gets altered when every term is increased by a fixed number. done
clear
D)
\[CV=\frac{SD}{AM}\times 100\] done
clear
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question_answer24)
Find the mode of the data: 2, 1, 5, 3, 4, 3, 5, 3, 6, 4, 5, 5, 3, 8.
A)
5 done
clear
B)
2 done
clear
C)
1 done
clear
D)
3 and 5 done
clear
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question_answer25)
Given that \[{{a}_{5}}+1={{a}_{6}}\] and median of \[{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{4}},{{a}_{5}},{{a}_{6}},{{a}_{7}},{{a}_{8}},{{a}_{9}},{{a}_{10}}\] is m, then find the median of the data \[{{a}_{3}},{{a}_{4}},{{a}_{5}},{{a}_{6}},{{a}_{7}},\] (where \[{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{4}},{{a}_{5}},{{a}_{6}},{{a}_{7}},{{a}_{8}},{{a}_{9}},{{a}_{10}}\] are arranged in ascending order).
A)
\[m\] done
clear
B)
\[\frac{m}{2}\] done
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C)
\[\frac{2m-1}{2}\] done
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D)
None of these done
clear
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question_answer26)
The of the 6, 3, 2, 2, 3, 6, 6, 3, 8, and x can be:
A)
Only 8 done
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B)
Both 3 and 6 done
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C)
Both 2 and 6 done
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D)
2, 3, or 6 done
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question_answer27)
If the difference between the mode and median is 8, then the difference between the median and mean is________. (in the given order).
A)
2 done
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B)
4 done
clear
C)
6 done
clear
D)
8 done
clear
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question_answer28)
If the SD of \[{{x}_{1}},{{x}_{2}},{{x}_{3}},.........{{x}_{n}}\] is 2.5 then find SD of \[{{x}_{1}}+3,{{x}_{2}}+3,{{x}_{3}}+3,.........{{x}_{n}}+3\].
A)
5.5 done
clear
B)
3 done
clear
C)
2.5 done
clear
D)
More data required done
clear
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question_answer29)
Direction: These are question are based on the following data:
Height (in cm) | Number of students |
160 | 12 |
165 | 4 |
170 | 6 |
175 | 8 |
180 | 10 |
Find the median of the above frequency distribution.
A)
165 done
clear
B)
170 done
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C)
160 done
clear
D)
180 done
clear
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question_answer30)
Direction: These are question are based on the following data:
Height (in cm) | Number of students |
160 | 12 |
165 | 4 |
170 | 6 |
175 | 8 |
180 | 10 |
The inter-quartile range of the above frequency distribution is_________.
A)
12 done
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B)
15 done
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C)
7.5 done
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D)
10 done
clear
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question_answer31)
If \[L=50,{{\Delta }_{1}}=8,{{\Delta }_{2}}=12\]and \[C=5\], then find the mode of the data; where \[{{\Delta }_{1}}={{f}_{m}}-{{f}_{m-1}}\] and \[{{\Delta }_{2}}={{f}_{m}}-{{f}_{m+1}},{{f}_{m}}=\] frequency of modal class, \[{{f}_{m-1}}=\] frequency of class before modal class, \[{{f}_{m+1}}=\] frequency of class after modal class, C = class width.
A)
48 done
clear
B)
52 done
clear
C)
53.5 done
clear
D)
54 done
clear
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question_answer32)
The mean and median of the data a, b and c are 130 and 120, where \[a<b<c\]. If \[c-a=60\], then find \[(b-c)\].
A)
5 done
clear
B)
35 done
clear
C)
60 done
clear
D)
- 45 done
clear
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question_answer33)
The given data are the times (in minutes), it takes seven students to go to school from their homes.
Which statements about the data are false?
A)
Their median is 12.5 done
clear
B)
Their mean is 13 done
clear
C)
Their range is 16 done
clear
D)
Their mode is 8 done
clear
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question_answer34)
What is the arithmetic mean of 20 fours, 40 fives, 30 sixes and 10 tens?
A)
50 done
clear
B)
25 done
clear
C)
5.6 done
clear
D)
33 done
clear
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question_answer35)
The mean of all factors of 36 is
A)
6.0 done
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B)
10.1 done
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C)
12 done
clear
D)
9.875 done
clear
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question_answer36)
Mean deviation of the data 3, 10, 10, 4, 7, 10, 5, from the mean is
A)
2 done
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B)
2.57 done
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C)
3 done
clear
D)
3.75 done
clear
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question_answer37)
A set of n values \[{{x}_{1}},{{x}_{2}}..........{{x}_{n}}\] has \[S.D.=\sigma \]. Then the S.D. of the values \[{{x}_{1}}+k,{{x}_{2}}+k,......,{{x}_{n}}+k\] will be
A)
\[\sigma \] done
clear
B)
\[\sigma +k\] done
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C)
\[\sigma -k\] done
clear
D)
\[k\sigma \]. done
clear
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question_answer38)
If the variance of the numbers 2, 4, 5, 6, 8, 17, is 23.33, then the variance of 4, 8, 10,12, 16, 34 will be
A)
23.33 done
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B)
46.66 done
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C)
93.32 done
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D)
None of these done
clear
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question_answer39)
The standard deviation of some temperature data in degree Celsius is 5, If data were converted into Fahrenheit, then the variance would be
A)
81 done
clear
B)
57 done
clear
C)
36 done
clear
D)
25 done
clear
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question_answer40)
Let \[{{x}_{1}},{{x}_{2}},.....,{{x}_{n}}\] be n observations. Let \[{{w}_{i}}=1{{x}_{i}}+k\] for = 1, 2, 3, ........ n where 1 and k are constants. If the mean of \[{{x}_{i}}s\]. is 48 and their S.D. is 12; the mean of \[{{w}_{i}}'s\] is 55 and their S. D. is 15, then the value of 1 and k are respectively
A)
1.25, 5 done
clear
B)
2, 5 done
clear
C)
2 - 5 done
clear
D)
1.25, - 5 done
clear
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