Mathematics

Use the adjoining table to find:
(i) upper and lower limits of fifth class.
(ii) true class limits of the fifth class.
(iii) class boundaries of the third class.
(iv) class mark of the fourth class.
(v) width of sixth class.
Class Frequency
28 - 32 5
33 - 37 8
38 - 42 13
43 - 47 9
48 - 52 7
53 - 57 5
58 - 62 2

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(i) Fifth class : 48 - 52

Hence, upper limit = 52 and lower limit = 48.

(ii) Adjustment factor = (Lower limit of class - Upper limit of previous class) / 2

= $\dfrac{48 - 47}{2} = \dfrac{1}{2}$ = 0.5

True lower limit = 48 - 0.5 = 47.5

True upper limit = 52 + 0.5 = 52.5

Hence, true class limits of fifth class = 47.5 and 52.5

(iii) Third class : 38 - 42

True lower limit = 38 - 0.5 = 37.5

True upper limit = 42 + 0.5 = 42.5

Hence, class boundaries of third class = 37.5 and 42.5

(iv) Fourth class : 43 - 47

Class mark = $\dfrac{\text{Lower class limit + Upper class limit}}{2}$

= $\dfrac{43 + 47}{2} = \dfrac{90}{2}$

= 45.

Hence, class mark of fourth class = 45.

(v) Fifth class : 53 - 57

True lower limit = 53 - 0.5 = 52.5

True upper limit = 57 + 0.5 = 57.5

Hence, width = 5.

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