Respuesta :
Answer:
(a) Mean = Â 72.1 Â Â Â Â Â Â Â Â Â Â Â Â Standard deviation = 6.14
(b) New Mean = Â 85.1 Â Â Â Â Â Â Â New Standard deviation = 6.14
Step-by-step explanation:
We are given the scores on a 100-mark test of a sample of 80 students in a large school;
 Score    No. of students (f)    X    X*f    [tex](X-Xbar)^{2}[/tex]    [tex]f*(X-Xbar)^{2}[/tex]
59 - 63 Â Â Â Â Â Â Â Â 6 Â Â Â Â Â Â Â Â Â Â Â 61 Â Â Â 366 Â Â Â Â Â 123.21 Â Â Â Â Â Â Â Â 739.26
63 - 67 Â Â Â Â Â Â Â Â 10 Â Â Â Â Â Â Â Â Â Â Â 65 Â Â Â 650 Â Â Â Â Â 50.41 Â Â Â Â Â Â Â Â 504.1
67 - 71 Â Â Â Â Â Â Â Â 18 Â Â Â Â Â Â Â Â Â Â Â 69 Â Â Â 1242 Â Â Â Â Â 9.61 Â Â Â Â Â Â Â Â Â 172.98
71 - 75 Â Â Â Â Â Â Â Â 24 Â Â Â Â Â Â Â Â Â Â 73 Â Â Â 1752 Â Â Â Â Â 0.81 Â Â Â Â Â Â Â Â Â 19.44
75 - 79 Â Â Â Â Â Â Â Â 10 Â Â Â Â Â Â Â Â Â Â Â 77 Â Â Â 770 Â Â Â Â Â 24.01 Â Â Â Â Â Â Â Â 240.1
79 - 83 Â Â Â Â Â Â Â Â 8 Â Â Â Â Â Â Â Â Â Â Â 81 Â Â Â 648 Â Â Â Â Â 79.21 Â Â Â Â Â Â Â Â 633.68
83 - 87 Â Â Â Â Â Â Â Â 4 Â Â Â Â Â Â Â Â Â Â Â 85 Â Â Â 340 Â Â Â Â 166.41 Â Â Â Â Â Â Â 665.64 Â Â
            ∑f = 80            ∑X*f = 5768           Total = 2975.2
(a) Mean of the above data, X bar = [tex]\frac{\sum Xf}{\sum f}[/tex] = [tex]\frac{5768}{80}[/tex] = 72.1
Standard deviation, s = [tex]\sqrt{\frac{\sum f*(X-Xbar)^{2} }{\sum f -1} }[/tex] = [tex]\sqrt{\frac{2975.2 }{80 -1} }[/tex] = 6.14
Therefore, mean and standard deviation of the scores of all students are 72.1 and 6.14 respectively.
(b) Now, a bonus of 13 points is to be added to these scores.
So, Mean will also increases by 13 points and due to this;
New Mean = 72.1 + 13 = 85.1
Adding 13 points to each score will not affect standard deviation and due to which New standard deviation is same as before of 6.14.
