from the following data , obtained from a sample of 1000 person ,calculate the standard error of the mean . Earings (in Rs) 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 and number of person 50,100,150,200,200,100,100,100 .If the average of population was Rs .42,what conclusion can you arrive at about reliability of the sample?
Answers
Answer:
Step-by-step explanation:
Solution :-
Earing (In Rs.) ------- Fi ---------- Xi ------------ FiXi
0 - 10 ------------------ 50 -------- 5 ------------- 250
10 - 20 ---------------- 100 ------ 15 ------------- 1500
20 - 30 ----------------150 --------25 ------------3750
30 - 40 ----------------200 ------ 35 ------------7000
40 - 50 ----------------200 -------45 ------------9000
50 - 60 ----------------100 ------ 55 ------------ 5500
60 - 70 ----------------100 --------65 ------------6500
70 - 80 ----------------100 ------ 75 -------------7500
⅀Fi = 1000 ⅀FiXi = 41000
so,
→ Mean = ⅀FiXi/⅀Fi = 41000/1000 = 41 = M
now,
Earing (In Rs.) ------- Fi ------(M -Xi)²-------Fi(M - Xi)²
0 - 10 ------------------ 50 ------1296 --------- 64800
10 - 20 ---------------- 100 ------676 --------- 67600
20 - 30 ----------------150 ------256 --------- 38400
30 - 40 ----------------200 ------36 ---------- 7200
40 - 50 ----------------200 -------16 ---------- 3200
50 - 60 ----------------100 ------196 ---------- 19600
60 - 70 ----------------100 -------576 ---------57600
70 - 80 ----------------100 ------1156 ----------115600
⅀Fi = 1000 ⅀Fi(M -Xi)² = 374000
then,
→ Standard deviation = √⅀Fi(M -Xi)² / (n - 1) = √(374000/999) = √(374.38) ≈ 19.35
therefore,
→ standard error of the mean = Standard deviation / √N = 19.35/√1000 = 19.35/31.62 ≈ 0.612 (Ans.)
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