In a class test marks obtained by 120 students are given in the following frequency distribution. If it is given that mean is 59 then find the frequencies x and y.
Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100
Frequency: 1, 3, 7, 10, 15, x, 9, 27, 18, y
Answers
Answer:
x = 29 and y = 1 are the frequencies
Step-by-step explanation:
Class Mid-point Frequency
0 - 10 5 1
10 - 20 15 3
20 - 30 25 7
30 - 40 35 10
40 - 50 45 15
50 - 60 55 x
60 - 70 65 9
70 - 80 75 27
80 - 90 85 18
90 - 100 95 y
It is given that the class has 120 students and is also equal to the sum of frequencies.
Therefore 1 + 3 + 7 + 10 + 15 + x + 9 + 27 + 18 + y = 120
Therefore x + y =30 .... (i)
Also we know that the mean of the data = 59.
Therefore (5×1) + (15×3) + (25×7) + (35×10) + (45×15) + (55x) + (65×9) + (75×27) + (85×18) + (95y) = 120×59
⇒ 5 + 45 + 175 + 350 + 675 + 55x + 585 + 2025 + 1530 + 95y = 7080
⇒ 55x + 95y = 1690
∴ 11x + 19y = 338 .... (ii)
Multiplying equation (i) by 11 we get
11x + 11y = 330 .... (iii)
Subtracting (iii) from (ii) we get 8y = 8. Therefore y = 1 .... (iv)
Using the value of y from (iv) in (i) we get x + 1 = 30 ∴ x = 29 .... (v)
Answer:
xi=5,15,25,35,45,55,65,75,85,95