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The class marks of a distribution are 61...

The class marks of a distribution are 61,66,71,76,81,86,91,96,101,106. Determine the class size, class limits and true class limits.

Text Solution

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Since class marks (mid values) are uniformly spaced, so the class-size is the differnce between any two consecutive class marks. Therefore, class size = 66-61 = 5
Let the lower limit of the first class be a.
`therefore "Its upper limit" =a+5`
Its mid value = 61
`therefore " Class mark" = "upper limit + lower limit"/(2)`
`rArr (a+(a+5))/(2)=61`
`implies a+(a+5)=122`
`implies 2a+5 = 122 rArr 2a-117 rArr a=58.5`
`therefore" The first class interval is " 58.5-63.5. " So, class intervals are "`

The above is the exclusive series. So, the true class limits are same as class limits.
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(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 lowe limit of the class. (iii)The width of each of the five continuous classes in a frequency distribution is 5 and lowe 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.