Answer:
[tex]Mean = 143[/tex]
Step-by-step explanation:
Given
Class-interval ---- Frequency
0 - 50 ----------------- 4
50 - 100 ------------- 8
100 - 150 ------------ 16
150 - 200 ------------- 13
200-250 ------------- 6
250-300 ------------- 3
Required
Determine the Mean
We start by calculating the midpoint (M) of the class interval
[tex]M = 0.5(L + U)[/tex]
Where:
[tex]L = Lower\ Interval[/tex]
[tex]U = Upper\ Interval[/tex]
Class-interval ---- ------Midpoint
0 - 50 --------------------0.5(0 + 50) = 25
50 - 100 ---------------- 0.5(50 + 100) = 75
100 - 150 ------------------ 0.5(100+150) = 125
150 - 200 -- ---------------- 0.5(150+200)=175
200-250 ------------------ 0.5(200+250) =225
250-300 ------------- 0.5 (250 + 300) = 275
Multiply the Midpoint by the corresponding frequency
Midpoint (M) ----- Frequency (F) ----- M* F
25 ------------------------ 4 ---------------------- 100
75 ------------------------- 8 --------------------- 600
125 ----------------------- 16 ---------------------2000
175 ----------------------- 13 --------------------- 2275
225 ----------------------- 6 --------------------- 1350
275 --------------------- 3 ------------------------- 825
Total -------------------50 ----------------------7150
Mean is then calculated as:
[tex]Mean = \frac{\sum MF}{\sum F}[/tex]
[tex]Mean = \frac{7150}{50}[/tex]
[tex]Mean = 143[/tex]
