Question 9
The following is the distribution of weights (in kg) of 40 persons.
$\begin{matrix} W e i g h t (i n k g) & 40 - 45 & 45 - 50 & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 & 75 - 80 N u m b e r o f p e r s o n s & 4 & 4 & 13 & 5 & 6 & 5 & 2 & 1 \end{matrix}$
Construct a cumulative frequency distribution (of the less than type) table for the data above.

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Solution

The cumulative distribution (less than type) table is shown below
$\begin{matrix} W e i g h t (i n k g) & C u m u l a t i v e f r e q u e n c y L e s s t h a n 45 & 4 L e s s t h a n 50 & 4 + 4 = 8 L e s s t h a n 55 & 8 + 13 = 21 L e s s t h a n 60 & 21 + 5 = 26 L e s s t h a n 65 & 26 + 6 = 32 L e s s t h a n 70 & 32 + 5 = 37 L e s s t h a n 75 & 37 + 2 = 39 L e s s t h a n 80 & 39 + 1 = 40 \end{matrix}$

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Question 7
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
$\begin{matrix} W e i g h t (i n k g) & 40 - 45 & 45 - 50 & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 N u m b e r o f s t u d e n t s & 2 & 3 & 8 & 6 & 6 & 3 & 2 \end{matrix}$

Q. The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

\begin{matrix} W e i g h t (i n k g) & 40 - 45 & 45 - 50 & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 N u m b e r o f s t u d e n t s & 2 & 3 & 8 & 6 & 6 & 3 & 2 \end{matrix}

Q. Question 13(i)
The following are the ages of 300 patients getting medical treatment in a hospital on a particular day

\begin{matrix} A g e (i n y e a r) & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 N u m b e r o f p a t i e n t s & 60 & 42 & 55 & 70 & 53 & 20 \end{matrix}

Form
(i) Less than type cumulative frequency distribution.

Q. The following are the ages of 300 patients getting medical treatment in a hospital on a particular day

\begin{matrix} A g e (i n y e a r) & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 N u m b e r o f p a t i e n t s & 60 & 42 & 55 & 70 & 53 & 20 \end{matrix}

Form:
More than type cumulative frequency distribution.

Q. Question 1
The following distribution gives the daily income of 50 workers of a factory.

\begin{matrix} D a i l y i n c o m e (i n R s) & 100 - 120 & 120 - 140 & 140 - 160 & 160 - 180 & 180 - 200 N u m b e r o f w o r k e r s & 12 & 14 & 8 & 6 & 10 \end{matrix}

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

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Question 9 The following is the distribution of weights (in kg) of 40 persons. Weight (in kg)40−4545−5050−5555−6060−6565−7070−7575−80Number of persons441356521 Construct a cumulative frequency distribution (of the less than type) table for the data above.

The cumulative distribution (less than type) table is shown below Weight(in kg)Cumulative frequencyLess than 454Less than 504+4=8Less than 558+13=21Less than 6021+5=26Less than 6526+6=32Less than 7032+5=37Less than 7537+2=39Less than 8039+1=40