The following distribution gives the monthly consumption of electricity in a locality of 80 families. If the median is 206, find the missing frequencies x and y. Please solve fast the fastest one will be marked the brainlies and also many points are rewarded please I need fast and accurate answer
Answers
Answer:
Hence, missing frequencies are x = 15 and y = 1
Step-by-step explanation:
Hi
"Monthly
Consumption
of electricity" Number of families Cumulative Frequency
170-180 4 4
180-190 x 4 + x
190-200 12 16 + x
200-210 15 31 + x
210-220 13 44 + x
220-230 y 44 + x + y
230-240 14 58 + x + y
240-250 6 64 + x + y
Since , given there are 80 families ,
64 + x + y = 80
=> x + y = 16-------(1)
median of grouped distribution =L+(N/2−C)/f×w
L = lower boundary of the median class
N = total frequency
C = cumulative frequency of the class preceding the median class
f = frequency of the median class
w = width of the median class i.e. upper boundary - lower boundary
Given median = 206
median class = 200-210
C = 16 + x
L = 200
N = 80
f =15
w = 10
Thus, 206 = 200 + (80/2 - 16 - x)/15*10
=> 6 = (24 - x)*2/3
=> 24 - x = 9
=> x = 15
Using (1), we get y = 1
Hence, missing frequencies are x = 15 and y = 1
Hope, it helps !