Question

Find out the arithmetic mean from the following : ITEMS : More than 0,More than 10,More than 20,More than 30. THEIR RESPECTIVE FREQUENCIES ARE: 28,24,14 and 4. *

Answer 1

Answer:

Here we have, the cumulative frequency distribution. So, first we convert it into an ordinary frequency distribution. we observe that are 80 students getting marks greater than or equal to 0 and 77 students have secured 10 and more marks. Therefore, the number of students getting marks between 0 and 10 is 80-77= 3.

Similarly, the number of students getting marks between 10 and 20 is 77-72= 5 and so on. Thus, we obtain the following frequency distribution.

Marks Number of students0-10310-20520-30730-401040-501250-601560-70 1270-80680-90290-1008Now, we compute mean arithmetic mean by taking 55 as the assumed mean.

Computative of Mean 

Marks

(xi)Mid-value (fi)Frequency ui10xi−55fiui0-1053-5-1510-20155-4-2020-30257-3-2130-403510-2-2040-504512-1-2050-6055150060-70651211270-8075621280-908523690-100958432Total          

       ∑fi=80∑fiui= -26

 We have,

N= sumfi=80,∑fiui=−26, A= 55 and h= 10 

∴X=A+h[N1∑fiui]

⇒X=A+h[N1∑fiui]

⇒X=55+10×80−26=55−3