Statistics Test

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Statistics Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

If ∑f_i = 15, ∑f_ix_i= 3p+36 and the mean of the distribution is 3, then the value of ‘p’ is

A
3

B
2

C
4

D
5

Solution

Mean \(=\frac{\sum f_{i} x_{i}}{\sum f_{i}}\)
\(\Rightarrow 3=\frac{3 p+36}{15}\)
\(\Rightarrow 3 p+36=45\)
\(\Rightarrow 3 p=45-36\)
\(\Rightarrow 3 p=9\)
\(\Rightarrow p=\frac{9} {3}\)
\(\Rightarrow p=3\)
Question 2
1 / -0

If xi′s are the midpoints of the class intervals of grouped data, fi′s are the corresponding frequencies and \(\bar{x}\) is the mean, then ∑(f_ix_i − \(\bar{x}\)) is equal to

A
– 1

B
1

C
0

D
2

Solution

Given that, \(x_{i}\) are the mid points of the class intervals.
\(f _{i}\) are the corresponding frequencies.
The mean \(\bar{x}\) for the grouped data is \(\bar{x}=\frac{\sum f_{i} x_{i}}{n}\)
\(\Longrightarrow \overline{ x } n =\sum f _{ i } x _{ i }\).........(1)
\(\sum\left(f_{i} x_{i}-\bar{x}\right)=\sum f_{i} x_{i}-\sum \bar{x}\)
\(\Longrightarrow \sum\left(f_{i} x_{i}-\bar{x}\right)=\bar{x} n-\sum \bar{x}(f r o m(1))\)
\(\Longrightarrow \sum\left(f_{i} x_{i}-\bar{x}\right)=\bar{x} n-\bar{x} n=0\)
Question 3
1 / -0

The marks obtained by 9 students in Mathematics are 59, 46, 31, 23, 27, 40, 52, 35 and 29. The mean of the data is

A
23

B
41

C
38

D
30

Solution

Given: 59,46,31,23,27,40,52,35 and 29
Mean \(=\frac{\text { Sum of all observations }}{\text { Number of oservation }}\)
\(=\frac{59+46+31+23+27+40+52+35+29}{9}\)
\(=\frac{342}{9}\)
\(=38\)
Question 4
1 / -0

The mean of the data when ∑ f_id_i= −500, ∑ f_i = 100 and a = 125 is

A
125

B
100

C
120

D
– 500

Solution

Mean \(=a+\frac{\sum f_{i} d_{i}}{\sum f_{i}}\)
\(=125+\frac{-500}{100}=125-5=120\)
Question 5
1 / -0

If ∑ f_iu_i= 29, ∑ f_i= 30, a = 47.5 and h = 15, then the value of x̄ is

A
26

B
64

C
62

D
63

Solution

\(\bar{x}=a+\frac{\sum f_{i} u_{i}}{\sum_{i}} \times h\)
\(=47.5+\frac{29}{30} \times 15\)
\(=47.5+\frac{29} {2}\)
\(=47.5+14.5\)
\(=62\)
Question 6
1 / -0

The mean of the first 10 prime numbers is

A
11.9

B
1.29

C
12.9

D
129

Solution

The first 10 prime numbers are 2,3,5,7,11,13,17 19,23,29
\(\therefore\) Mean \(=\frac{\text { Sum of first } 10 \text { prime numbers }}{10}\) \(=\frac{2+3+5+7+11+13+17+19+23+29}{10}\)
\(=\frac{129}{10}\)
\(=12.9\)
Question 7
1 / -0

If ∑ f_i=17, ∑ f_ix_i=4p + 63 and the mean of the distribution is 7, then the value of ‘p’ is

A
13

B
14

C
15

D
12

Solution

since, Mean \(=\frac{\sum f_{i} x_{i}}{\sum f_{i}}\)
\(\Rightarrow 7=\frac{4 p+63}{17}\)
\(\Rightarrow 4 p+63=119\)
\(\Rightarrow 4 p=119-63\)
\(\Rightarrow 4 p=56\)
\(\Rightarrow p=14\)
Question 8
1 / -0

∑ (x_i − x̄) is equal to

A
1

B
2

C
0

D
– 1

Solution

\(\sum x_{i}-\bar{x}=\sum x_{i}-\sum(\bar{x})\)
\(\sum(\bar{x})= n (\bar{x})\) by definition
But \(\bar{x}=\left(\sum x_{i}\right) / n\) by definition
so \(\sum x_{i}-\sum(\bar{x})=\sum x_{i}- n \left(\left(\sum x_{i}\right) / n\right)\)
which is equal to \(=\left(\sum x_{i}\right)-\left(\sum x_{i}\right)=0\)
Question 9
1 / -0

If ∑f_ix_i = 1860 and ∑f_i = 30, then the value of \( \bar{x}\) is

A
26

B
63

C
62

D
64

Solution

\(\bar{x}=\frac{\sum f_{i} x_{i}}{\sum f_{i}}\)
\(=\frac{1860}{30}\)
\(=62\)
Question 10
1 / -0

The mean of the first 10 natural numbers is

A
6

B
5

C
5.5

D
4.5

Solution

The first 10 natural numbers are \(1,2,3, \ldots \ldots \ldots, 10\) \(\therefore\)
Mean \(=\frac{\text { Sum of first } 10 \text { natural numbers }}{10}\)
\(=\frac{1+2+3+\ldots \ldots+10}{10}\)
\(=\frac{55}{10}\)
\(=5.5\)
Question 11
1 / -0

The mean of first 10 composite numbers is

A
12.2

B
11.4

C
11.2

D
112

Solution

The first 10 composite numbers are 4,6,8,9,10,12 , 14,15,16,18
\(\therefore\) Mean \(=\frac{\text { Sum of first } 10 \text { composite numbers }}{10}\) \(=\frac{4+6+8+9+10+12+14+15+16+18}{10}\)
\(=\frac{112}{10}\)
\(=11.2\)

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Re-Attempt Weekly Quiz Competition

Statistics Test - 13

Result

Statistics Test - 13

Score

-

Rank

-

SHARING IS CARING

Question 1

3

2

4

5

Solution

Question 2

– 1

1

0

2

Solution

Question 3

23

41

38

30

Solution

Question 4

125

100

120

– 500

Solution

Question 5

26

64

62

63

Solution

Question 6

11.9

1.29

12.9

129

Solution

Question 7

13

14

15

12

Solution

Question 8

1

2

0

– 1

Solution

Question 9

26

63

62

64

Solution

Question 10

6

5

5.5

4.5

Solution

Question 11

12.2

11.4

11.2

112

Solution

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