Question

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

Answer 1

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 !