Question

Question 1

The marks obtained by 30 students in a subject are given below:
15,20,21,22,35,40,45,16,31,22,26,29,18,41,49,43,48,23,28,32,36,38,24,29,30,46,42,44,25,50
Arrange the data into 8 classes with equal class interval and then find the mean of this grouped data.

Question 2
Find the quartile deviation of the following data.

         10, 25, 11, 19, 10, 29, 15, 14, 17

Answer 1

1)

To form 8 classes, the class interval is found as follows

Class interval Highest value - lowest value 50 - 15 number of classes 8

Class interval = 5

Marks Number of students 3 15.-20 20.-25 25.-30 30.-35 6 5 3 35.-40 3 40.-45 5 4 45.-50 50.-55 1

The mean of the above grouped data is found as follows

Marks 52.5 15.-20 20.-25 25.-30 Number of students Midpoint (X) |FX 3 17.5 6 22.5 5 27.5 3 32.5 30.-35 35.-40 40.-45 135 137.5 97.5 112.5 212.5 3 37.5 5 45.-50 4 42.5 47.5 52.5 190 50.-55 1 52.5 FX = 990

990 Mean X- ΣFX N 30

Mean of the grouped data = 33

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2)

Cumulative frequency Data 2 Frequency 10 2 11 1 14 1 15 1 3 4 5 17 1 6 19 1 7 25 1 8 29 1 9

03-01 Quartile deviation

Q1 = first quartile

Q3 = third quartile

Q3 = ( 3N $\div$ 4) observation = ( 3 $\times$ 9 ) $\div$ 4 = 6.75 or 7th observation = 19

Q1 = ( N $\div$ 4 ) = ( 9 $\div$ 4 ) = 2.25 or 3rd observation = 11

Quartile deviation 19 - 11 2

Quartile deviation = 4