Q10 of 43 Page 293

Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:

For some data Z — M = 2.5. If the mean of the data is 20, then Z =


We have been given that,

Z – M = 2.5


⇒ M = Z – 2.5 …(i)


And …(ii)


Here, Z = Mode,


M = Median


&


So, by empirical relationship we have,


Mode = 3 (Median) – 2 (Mean)


⇒


Putting equations (i) and (ii) in the above equation, we get


Z = 3(Z – 2.5) – 2×20


⇒ Z = 3Z – 7.5 – 40


⇒ 3Z – Z = 40 + 7.5


⇒ 2Z = 47.5


⇒


⇒ Z = 23.75


Thus, option (c) is correct.

More from this chapter

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9

The median of the following data is 525. Find the value of x and y, if the sum of frequency is 100.





























Class



0-100



100-200



200-300



300-400



400-500



500-600



600-700



700-800



800-900



900-1000



Frequency



3



4



x



12



17



20



9



y



8



3



 10

Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:

For some data, if Z = 25 and = 25, then M =


10

Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:

If — Z = 3 and + Z = 45, then M =


 10

Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:

If Z = 24, = 18, then M=