Mathematics, 24.02.2020 08:26, laykaleb086

The scores on a 100-mark test of a sample of 80 students in a large school are given in the table.

SCORE: 59-63 63-67 67-71 71-75 75-79 79-83 83-87
# OF STUDENTS: 6 10 18 24 10 8 4

a) Find the mean and standard deviation of the scores of all students.

b) A bonus of 13 points is to be added to these scores. What is the new value of the mean and standard deviation?

Answers: 3

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Answers

answered: swaggernas

(a) Mean = 72.1 Standard deviation = 6.14

(b) New Mean = 85.1 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 $(X-Xbar)^{2}$ $f*(X-Xbar)^{2}$

59 - 63 6 61 366 123.21 739.26

63 - 67 10 65 650 50.41 504.1

67 - 71 18 69 1242 9.61 172.98

71 - 75 24 73 1752 0.81 19.44

75 - 79 10 77 770 24.01 240.1

79 - 83 8 81 648 79.21 633.68

83 - 87 4 85 340 166.41 665.64

∑f = 80 ∑X*f = 5768 Total = 2975.2

(a) Mean of the above data, X bar = $\frac{\sum Xf}{\sum f}$ = $\frac{5768}{80}$ = 72.1

Standard deviation, s = $\sqrt{\frac{\sum f*(X-Xbar)^{2} }{\sum f -1} }$ = $\sqrt{\frac{2975.2 }{80 -1} }$ = 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.

answered: Guest

The correct answer will be d. -4

answered: Guest

38 dollars is your answer.

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The scores on a 100-mark test of a sample of 80 students in a large school are given in the table. <...