find the missing frequencies f1 and f2 in table given below; it is being given that the mean of the given frequency distribution is 145.
Answers
Answer:
f2 = 25
f1 = 25.
Step-by-step explanation:
From the table, the sub of frequencies is 80.
That is
10 + f1 + f2 + 15 + 5 = 80
f1 + f2 = 50. --------------------------------- 1 Equation.
The mean of the frequency distribution is 145.
That is
∑class*frequency / (∑Frequency) = 145.
The class has got a range, instead of single value.
(Like 100 to 120, 120 to 140 etc.)
Hence we need to take average of the value.
(110*10 + 130*f1 + 150*f2 + 170*15 + 190*5) / 80 = 145
130*f1 + 150*f2 = 7000
13*f1 + 15*f2 = 700 ----------------------------- 2 Equation
Multiplying first equation with 13 and subtracting from equation 2 gives us
13*f1 + 15*f2 = 700
13*f1 + 13*f2 = 650
2*f2 = 50
f2 = 25
Thus we get f1 = 25.
Answer:
f1 = 25
f2 = 25
Step-by-step explanation:
100 - 120 10
120 - 140 f1
140-160 f2
160-180 15
180- 200 5
Total = 80
10 + f1 + f2 + 15 + 5 = 80
=> f1 + f2 = 80 - 30
=> f1 + f2 = 50 - eq 1
100 - 120 , mean = (100 + 120)/2 = 110
frequency = 10
so SubTotal = 110 * 10 = 1100
Similarly
120-140 SubTotal = 130 * f1
140 -160 SubTotal = 150 * f2
160-180 SubTotal = 170*15 = 2550
180 - 200 SubTotal = 190*5 = 950
Total = 1100 + 130f1 + 150f2 + 2550 + 950 = 4600 + 130f1 + 150f2
Total frequencies = 80
Mean = Total / Total Freqeuncies
=> 145 = (4600 + 130f1 + 150f2)/80
=> 11600 = 4600 + 130f1 + 150f2
=> 130f1 + 150f2 = 7000
=> 13f1 + 15f2 = 700 - eq 2
Eq 2 - 13Eq1
13f1 + 15f2 - 13f1 - 13f2 = 700 - 650
=> 2f2 = 50
=> f2 = 25
Putting in eq 1
f1 + 25 = 50
=> f1 = 25