Question

median
the following tobls gives the distribution of wages of 900 warkes . however the freavuency are two class 40-50 and 60-70 are missing if the median of the distribution is 59.25
find the messing freavuency
wages: 30-40 , 40-50, 50-60, 60-70, 70-80
no.of warkes: 120 , ?,200,?,185
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CBSE

Mathematics

Grade 11

Measures of Central Tendency

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The median and mode of the following distribution are 33.5 and 34 rupees respectively. Find the missing frequencies.

Daily wages (in Rs.) 0-10 10-20 20-30 30-40 40-50 50-60 60-70 N

Frequencies 4 16 60 x y z 4 230

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Hint: From the table we will first form an equation corresponding to the sum of all frequencies. Then we will use the formula of median given by Median=l+⎛⎝⎜⎜N2−c.f.f⎞⎠⎟⎟×h and formula of mode given by Mode=l+(f1−f02f1−f0−f2)×h

to form equations. Solve the equations to find the value of x , y and z.

Complete step-by-step answer:

We are given, that the sum of frequencies is 230.

Form as equation corresponding to the given condition.

Write the sum of frequencies in the form of an equation.

4+16+60+x+y+z+4=230

Add the numbers on the left side of the equation.

84+x+y+z=230

After subtracting 84 from both sides, we get,

x+y+z=146 (1)

Add the previous frequencies to form the table with cumulative frequencies.

Daily wages (in Rs.) 0-10 10-20 20-30 30-40 40-50 50-60 60-70 N

Frequencies 4 16 60 x y z 4 230

Cumulative frequency (c.f.) 4 20 80 80+x 80+x+y 80+x+y+z 84+x+y+z

We are given that the median of the data is 33.5, this implies that the median class for the given data is 30-40.

Substitute the values in the formula of median, Median=l+⎛⎝⎜⎜N2−c.f.f⎞⎠⎟⎟×h, where l is the lower class limit of the median class, N is the total number, c.f. refers to the cumulative frequency of the previous class, and f refers to the frequency of the class and his the width of the class interval.

On substituting the values, we get,

33.5=30+⎛⎝⎜⎜2302−80x⎞⎠⎟⎟×10