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Question

# (i) Find the class mark of the class 90-120. (ii) In a frequency distribution, the mid-value of the class is 10 and width of the class is 6. Find the lower limit of the class. (iii) The width of each of five continuous classes in a frequency distribution is 5 and lower class limit of the lowest class is 10. What is the upper class limit of the highest class? (iv) The class marks of a frequency distribution are 15, 20, 25, .... Find the class corresponding to the class mark 20. (v) In the class intervals 10-20, 20-30, find the class in which 20 is included.

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Solution

## (i) class mark =upper limit+lower limit/2=120+90/2=105 (ii) mid-value = 10 width = 6 Let the lower limit of the class be x. upper limit = x + 6 class mark/mid - value =upper limit+lower limit/2 x+ (x+6 )/2=10 ⇒ x = 7 (iii) width = 5 lower class limit of lowest class = 10 The classes will be 10-15, 15-20, 20-25, 25-30, 30-35. Upper class limit of the highest class = 35. (iv) Class marks = 15, 20, 25, ...class size = 20 - 15 = 5 Let lower limit of class be x. x+ (x+5 )/2=20 ⇒ x = 17. 5 Thus, the class is 17.5-22.5. (v) 20 will be included in the class interval 20-30.

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