FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.9Example 11 : Find A.M. of the following distributions :
` c.f. Marks c.f.
(i) less than 4 2 (ii) More than 0 and above 10
less than 8 6 More than 5 and above 8
less than 12 13 More than 10 and above 5
less than 16 18 More than 15 and above 1
less than 20 20 More than 20 and above 0
(i) The difference between any two variables is 4; so the width of class-intervals will be 4.
Accordingly, we get the general group frequency distribution as follows :
Solution:
Table : Calculation of A.M.
f x f d =(x–A) fd
0–4 2 0–4 2 2 –8 –16
4–8 4(=6–2) 4–8 6 4 –4 –16
8–12 7(=13–6) 8–12 10 = (A) 7 0 0
12–16 5 (= 18–13) 12–16 14 5 4 20
16–20 2 (= 20 –18) 16 –20 18 2 8 16
Total –– 20 –– 4
Let A = 10
x = A + fd=10 +^4 = 10 + 0 2 10 2
f^20 ⋅ = ⋅
`Table : Calculation of A.M.
Marks f Marks. x f d d ́ fd ́
0–5 2 (=10–8) 0–5 2.5 2 –5 –1 –2
5–10 3 (= 8 –5) 5–10 7.5 3 0 0 0
10–15 4 (=5–1) 10 –15 12.5 4 + 5 1 4
15–20 1(= 1–0) 15–20 17.5 1 +10 2 2
Total –– 10 –– –– 4
Let A = 7.5A.M. =
A fd ́
f
+∑
∑ × i = 7.5 +4
10 × 5 = 7.5 + 2 = 9.5 marks.5.1.1.5. Advantages of Arithmetic Mean
(i) It is easy to calculate and simple to understand.