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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Answer from: 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.

Answer from: Quest

b mark me branliest thx

step-by-step explanation:

Answer from: Quest

answer: input the dimensions of the room to be painted. click the button to calculate the amount of paint and man-hours needed for this job.

interior paint coverage depends on the brand of paint used. the coverage amount is listed on the label of the paint can. use this to adjust the values in the paint coverage section below. paint usually is applied at 350 to 400 square feet per gallon (primer at 200 to 300 square feet per gallon).

step-by-step explanation:

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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. <...