Past papers › NECO · 2023 · SSCE · Further Maths · Paper 2 › Question 6 Question NECO Further Maths 2023 Theory Statistics & correlation Statistics & correlation
The table shows the distribution of marks obtained by 100 candidates in an examination. Calculate, correct to three significant figures, the standard deviation.
Marks
1–10
11–20
21–30
31–40
41–50
Frequency
9
49
32
8
2
Worked solution (try it first) Class marks:
5.5 , 15.5 , 25.5 , 35.5 , 45.5 5.5, 15.5, 25.5, 35.5, 45.5 5.5 , 15.5 , 25.5 , 35.5 , 45.5 .
Take
A = 25.5 A = 25.5 A = 25.5 , so
d = − 20 , − 10 , 0 , 10 , 20 d = -20, -10, 0, 10, 20 d = − 20 , − 10 , 0 , 10 , 20 .
∑ f d = 9 ( − 20 ) + 49 ( − 10 ) + 0 + 8 ( 10 ) + 2 ( 20 ) \sum fd = 9(-20) + 49(-10) + 0 + 8(10) + 2(20) ∑ f d = 9 ( − 20 ) + 49 ( − 10 ) + 0 + 8 ( 10 ) + 2 ( 20 ) ∑ f d 2 = 9 ( 400 ) + 49 ( 100 ) + 0 + 8 ( 100 ) + 2 ( 400 ) \sum fd^2 = 9(400) + 49(100) + 0 + 8(100) + 2(400) ∑ f d 2 = 9 ( 400 ) + 49 ( 100 ) + 0 + 8 ( 100 ) + 2 ( 400 ) σ = 10 100 100 − ( − 550 100 ) 2 \sigma = \sqrt{\dfrac{10\,100}{100} - \left(\dfrac{-550}{100}\right)^2} σ = 100 10 100 − ( 100 − 550 ) 2 = 101 − 30.25 = \sqrt{101 - 30.25} = 101 − 30.25 = 70.75 = \sqrt{70.75} = 70.75 Watch out
Use the class marks (mid-values) as x x x Subtract the square of ∑ f d ∑ f \frac{\sum fd}{\sum f} ∑ f ∑ f d Report a problem with this question