Moderate 784 likes
Share

Question

If the arithmetic mean and total frequency of the following distribution are 50 and 120 respectively, then find the value of f1 and f2:

Class Frequency
0 – 20 17
20 – 40 f1
40 – 60 32
60 – 80 f2
80 – 100 19
WBBSE Class X Mathematics Statistics 04 Mark 2023

Answer

Class x f fx
0 – 20 10 17 170
20 – 40 30 f1 30f1
40 – 60 50 32 1600
60 – 80 70 f2 70f2
80 – 100 90 19 1710
Total 68 + f1 + f2 3480 + 30f1 + 70f2

Σf = 120

or, 68 + f1 + f2 = 120

or, f1 + f2 = 120 – 68

or, f1 + f2 = 52 — (1)

Σfx = mean × Σf

or, 3480 + 30f1 + 70f2 = 50 × 120

or, 30f1 + 70f2 = 2520

or, 3f1 + 7f2 = 252 — (2)

Solving (1) and (2), we get

f1 = 28

and  f2 = 24

Hence, the values of f1 and f2 are 28 and 24.

Related Questions

More WBBSE Moderate level questions

1/12
Moderate
983
Q. Find the mode of the following frequency distribution :
A. Class Class boundary Frequency 50 - 59 49.5 - 59.5 5 60...
View Question
Moderate
808
Q. Draw an ogive on the graph paper after calculating the cumulative frequency (less than type)...
A. Class Interval Frequency CF 0 - 10 1 1 10 - 20...
View Question
Moderate
637
Q. The median of following data is 32. Find the value of x and y if...
A. Class Interval Frequency (f) CF 0 - 10 10 10 10 -...
View Question
Moderate
578
Q. Find the median of the data from the following distribution
A. Class int Class boundary frequency (f) CF 0 - 9 0 -...
View Question
Moderate
687
Q. Find the mode from the following data
A. The class with the highest frequency is 20 – 25, so it...
View Question
Easy
761
Q. Construct the table of cumulative frequency (greater than type) and draw the ogive from the...
A. Class Cummulative Frequency Greater than 0 100 Greater than 10 93 Greater...
View Question
Moderate
920
Q. 27, 31, 46, 52, x, y + 2, 71, 79, 85, 90 are in increasing...
A. (d) 126 Explanation: n = 10 (even) median = or, 64 =...
View Question
Easy
980
Q. If 6, 8, 10, 12, 13, x are in increasing order and their mean and...
A. Numbers in ascending order are 6, 8, 10, 12, 13, x Mean...
View Question
Easy
938
Q. State True or False: The Mode of the data 5, 2, 4, 3, 5, 2,...
A. False Explanation the mode is 2 as well as 5
View Question
Easy
749
Q. The median of the numbers 8, 15, 10, 11, 7, 9, 11, 13 and 16...
A. 11 Explanation 7, 8, 9, 10, 11, 11, 13, 15, 16 Here...
View Question
Easy
809
Q. Three values ​​of a variable are 4, 5 and 7, if their frequencies are p...
A. (d) 4 Explanation Mean = or, 5.4 = or, 5.4 = or,...
View Question
Easy
644
Q. The age of 100 persons present in a workshop is given in the following table....
A. Age Group Number of People (f) Midpoint (x) fx 10 - 20...
View Question