Answer:
The standard deviation of the given data is 11.34.
Step-by-step explanation:
We have to find the standard deviation for the given data;
Grade on No. of students
test (X) with that score (f) [tex]X \times f[/tex] [tex]( X - \bar X)^{2}[/tex] [tex]f \times ( X - \bar X)^{2}[/tex]
50 1 50 1073.218 1073.2176
57 2 114 663.578 1327.1552
60 4 240 518.018 2072.0704
65 3 195 315.418 946.2528
72 3 216 115.778 347.3328
75 12 900 60.218 722.6112
77 10 770 33.178 331.776
81 6 486 3.098 18.5856
83 6 498 0.058 0.3456
88 9 792 27.458 247.1184
90 12 1080 52.418 629.0112
92 12 1104 85.378 1024.5312
95 2 190 149.818 299.6352
99 4 396 263.738 1054.9504
100 5 500 297.218 1486.088
Total 91 7531 11580.68
Firstly, the mean of the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X \times f}{\sum f}[/tex]
= [tex]\frac{7531}{91}[/tex] = 82.76
Now, the standard deviation of the data is given by;
Standard deviation, S.D. = [tex]\sqrt{\frac{\sum f(X-\bar X)^{2} }{\sum f-1}}[/tex]
= [tex]\sqrt{\frac{11580.68}{91-1}}[/tex]
= 11.34
Hence, the standard deviation of the given data is 11.34.
