Scroll:Statistics >> Direct Method >> saq (4238)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

 Using assumed mean method find the mean weight of 56 students using the data given below.

weight in kg 43 46 56 57 62
No. of students 18 16 10 9 3


 


Answer:_______________




2)  

 Using assumed mean method find the mean weight of 58 students using the data given below.

weight in kg 40 50 52 57 65
No. of students 18 15 13 9 3


 


Answer:_______________




3)  

 Using assumed mean method find the mean weight of 53 students using the data given below.

weight in kg 45 48 55 60 63
No. of students 17 15 11 6 4


 


Answer:_______________




4)  

 Using assumed mean method find the mean weight of 57 students using the data given below.

weight in kg 40 48 51 59 62
No. of students 17 16 12 9 3


 


Answer:_______________




5)  

 Using assumed mean method find the mean weight of 56 students using the data given below.

weight in kg 42 48 54 57 65
No. of students 17 16 10 8 5


 


Answer:_______________




6)  

 Using assumed mean method find the mean weight of 59 students using the data given below.

weight in kg 42 47 52 59 65
No. of students 18 16 12 8 5


 


Answer:_______________




7)  

 Using assumed mean method find the mean weight of 53 students using the data given below.

weight in kg 44 46 51 58 65
No. of students 17 16 11 6 3


 


Answer:_______________




8)  

 Using assumed mean method find the mean weight of 57 students using the data given below.

weight in kg 45 46 56 60 61
No. of students 18 16 11 8 4


 


Answer:_______________




9)  

 Using assumed mean method find the mean weight of 60 students using the data given below.

weight in kg 41 49 53 57 61
No. of students 17 16 13 9 5


 


Answer:_______________




10)  

 Using assumed mean method find the mean weight of 52 students using the data given below.

weight in kg 45 50 52 57 62
No. of students 17 16 10 6 3


 


Answer:_______________




 

1)  

 Using assumed mean method find the mean weight of 56 students using the data given below.

weight in kg 43 46 56 57 62
No. of students 18 16 10 9 3

Answer: 49.45

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

43

46

56=A

57

62

18

16

10

9

3

 -13

-10

0

1

6

-234

-160

0

9

18 

 56   -367

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
56
 
+
 		(-367)
(56)
 

 

= 56 + (-6.55)

= 49.45



2)  

 Using assumed mean method find the mean weight of 58 students using the data given below.

weight in kg 40 50 52 57 65
No. of students 18 15 13 9 3

Answer: 49.21

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

40

50

52=A

57

65

18

15

13

9

3

 -12

-2

0

5

13

-216

-30

0

45

39 

 58   -162

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
52
 
+
 		(-162)
(58)
 

 

= 52 + (-2.79)

= 49.21



3)  

 Using assumed mean method find the mean weight of 53 students using the data given below.

weight in kg 45 48 55 60 63
No. of students 17 15 11 6 4

Answer: 50.98

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

45

48

55=A

60

63

17

15

11

6

4

 -10

-7

0

5

8

-170

-105

0

30

32 

 53   -213

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
55
 
+
 		(-213)
(53)
 

 

= 55 + (-4.02)

= 50.98



4)  

 Using assumed mean method find the mean weight of 57 students using the data given below.

weight in kg 40 48 51 59 62
No. of students 17 16 12 9 3

Answer: 48.72

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

40

48

51=A

59

62

17

16

12

9

3

 -11

-3

0

8

11

-187

-48

0

72

33 

 57   -130

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
51
 
+
 		(-130)
(57)
 

 

= 51 + (-2.28)

= 48.72



5)  

 Using assumed mean method find the mean weight of 56 students using the data given below.

weight in kg 42 48 54 57 65
No. of students 17 16 10 8 5

Answer: 50.05

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

42

48

54=A

57

65

17

16

10

8

5

 -12

-6

0

3

11

-204

-96

0

24

55 

 56   -221

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
54
 
+
 		(-221)
(56)
 

 

= 54 + (-3.95)

= 50.05



6)  

 Using assumed mean method find the mean weight of 59 students using the data given below.

weight in kg 42 47 52 59 65
No. of students 18 16 12 8 5

Answer: 49.64

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

42

47

52=A

59

65

18

16

12

8

5

 -10

-5

0

7

13

-180

-80

0

56

65 

 59   -139

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
52
 
+
 		(-139)
(59)
 

 

= 52 + (-2.36)

= 49.64



7)  

 Using assumed mean method find the mean weight of 53 students using the data given below.

weight in kg 44 46 51 58 65
No. of students 17 16 11 6 3

Answer: 48.83

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

44

46

51=A

58

65

17

16

11

6

3

 -7

-5

0

7

14

-119

-80

0

42

42 

 53   -115

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
51
 
+
 		(-115)
(53)
 

 

= 51 + (-2.17)

= 48.83



8)  

 Using assumed mean method find the mean weight of 57 students using the data given below.

weight in kg 45 46 56 60 61
No. of students 18 16 11 8 4

Answer: 50.63

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

45

46

56=A

60

61

18

16

11

8

4

 -11

-10

0

4

5

-198

-160

0

32

20 

 57   -306

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
56
 
+
 		(-306)
(57)
 

 

= 56 + (-5.37)

= 50.63



9)  

 Using assumed mean method find the mean weight of 60 students using the data given below.

weight in kg 41 49 53 57 61
No. of students 17 16 13 9 5

Answer: 49.80

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

41

49

53=A

57

61

17

16

13

9

5

 -12

-4

0

4

8

-204

-64

0

36

40 

 60   -192

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
53
 
+
 		(-192)
(60)
 

 

= 53 + (-3.20)

= 49.80



10)  

 Using assumed mean method find the mean weight of 52 students using the data given below.

weight in kg 45 50 52 57 62
No. of students 17 16 10 6 3

Answer: 50.25

 


SOLUTION 1 :

 

weights in kgf d = x-A fd

45

50

52=A

57

62

17

16

10

6

3

 -7

-2

0

5

10

-119

-32

0

30

30 

 52   -91

 

-
x
 
=
 
A
 
+
 		∑ fd
∑ f

 

-
x
 
=
 
52
 
+
 		(-91)
(52)
 

 

= 52 + (-1.75)

= 50.25