Question
Construct a frequency distribution table from the given cumulative frequency distribution showing the weights of $750$ students in a school:
Weight $($in $kg)$ $c.f.$
More Than$ 25$ $750$
More Than $30$ $640$
More Than $35$ $615$
More Than $40$ $485$
More Than $45$ $370$
More Than $50$ $220$
More Than $55$ $124$
More Than $60$ $49$
More Than $65$ $24$
More Than $70$ $0$
$a$. Find the number of students whose weight lie in the interval $40-45;b$. Find the interval which has the most number of students.

Answer

Frequency distribution table is as follows:
Weight $($in $kg)$ $c.f.$
$25 - 30$ $110 (750 - 640)$
$30 - 35$ $25 (640 - 615)$
$35 - 40$ $130 (615 - 485)$
$40 - 45$ $115 (485 - 370)$
$45 - 50$ $150 (370 - 220)$
$50 - 55$ $96 (220 - 124)$
$55 - 60$ $75 (124 - 49)$
$60 - 65$ $25 (49 - 25)$
$65 - 70$ $24 (24 - 0)$
$70 - 75$ $0$
$a$. The number of students whose weight lie in the interval $40 - 45$ is $115.$
$b$. The interval $45 - 50$ has the most number of students.

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