Solution: (i) (ii)
Construct a frequency distribution table for the number given below, using the class intervals 21-30, 31-40 … etc. 75, 67, 57, 50, 26, 33, 44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36, 47 Use the table obtained to draw:
Draw an ogive for each of the following distributions:
(i) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Marks Obtained & less than 10 & less & less & less & less \\ \hline No. of Students & 8 & 25 & 38 & 50 & than 50 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Age in years (less than) & 10 & 20 & 30 & 40 & 50 & 60 & 70 \\ \hline Cumulative Frequency & 0 & 17 & 32 & 37 & 53 & 58 & 65 \\ \hline \end{tabular}$$
Solution: (i) $$\begin{tabular}{|l|l|} \hline Marks Obtained & No. of students (c.f.) \\ \hline less than 10 & 8 \\ \hline less than 20 & 25 \\ \hline less than 30 & 38 \\ \hline less than 40 & 50...
Draw cumulative frequency curve (ogive) for each of the following distributions:
(i) $$\begin{tabular}{|l|l|l|l|l|l|l|} \hline Class Interval & $10-15$ & $15-20$ & $20-25$ & $25-30$ & $30-45$ & $35-40$ \\ \hline Frequency & 10 & 15 & 17 & 12 & 10 & 08 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $10-19$ & $20-29$ & $30-39$ & $40-49$ & $50-59$ \\ \hline Frequency & 23 & 16 & 15 & 20 & 12 \\ \hline \end{tabular}$$
Solution: (i) $$\begin{tabular}{|l|l|} \hline Class Interval & Frequency \\ \hline 10-15 & 10 \\ \hline 15-20 & 15 \\ \hline 20-25 & 17 \\ \hline 25-30 & 12 \\ \hline $30-35$ & 10 \\ \hline $35-40$...
Draw histograms for the following frequency distributions:
(i) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $30-39$ & $40-49$ & $50-59$ & $60-69$ & $70-79$ \\ \hline Frequency & 24 & 16 & 09 & 15 & 20 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Class Marks & 16 & 24 & 32 & 40 & 48 & 56 & 64 \\ \hline Frequency & 8 & 12 & 15 & 18 & 25 & 19 & 10 \\ \hline \end{tabular}$$
Solution: (i) $$\begin{tabular}{|l|l|l|} \hline Class Interval (Inclusive form) & Class Interval (Exclusive Form) & Frequency \\ \hline $30-39$ & 29.5-39.5 & \\ \hline $40-49$ & 39.5-49.5 & 24 \\...
Draw histograms for the following frequency distributions:
(i) $$\begin{tabular}{|l|ccccc|c|} \hline Class Interval & $0-10$ & $10-20$ & $20-30$ & $30-40$ & $40-50$ & $50-60$ \\ \hline Frequency & 12 & 20 & 26 & 18 & 10 & 6 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $10-16$ & $16-22$ & $22-28$ & $28-34$ & $34-40$ \\ \hline Frequency & 15 & 23 & 30 & 20 & 16 \\ \hline \end{tabular}$$
Solution: (i) $$\begin{tabular}{|l|l|} \hline Class Interval & Frequency \\ \hline $0-10$ & 12 \\ \hline 10-20 & 20 \\ \hline 20-30 & 26 \\ \hline $30-40$ & 18 \\ \hline 40-50 & 10 \\ \hline 50-60 &...
Construct an ogive for the following:(vii)
Marks (more than)$0$$10$$20 $$30$$40$$50$$60$$70$$80$$90$$100$Cumulative Frequency$100$$87$$65$$55$$42$$36$$31$$21$$18$$7$$0$ Steps to draw a histogram for given frequency distributions, 1. Subtract...
Construct an ogive for the following:(v)
Age in yearsLess than 10Less than 20Less than 30Less than 40Less than 50Number of people$0$$17$$42$$67$$100$ (vi) Marks obtainedMore than 10More than 20Less than 30Less than 40Less than 50Number of...
Construct an ogive for the following:(iii)
Class Interval$10–19$$20–29$$30–39$$40–49$$50–59$Frequency$28$$23$$15$$20$$14$ (iv) Marks obtainedLess than 10Less than 20Less than 30Less than 40Less than 50Number of Students$8$$22$$48$$60$$75$...
Construct an ogive for the following:(i)
Class Interval$0–10$$10–20$$20–30$$30–40$$40–50$Frequency$8$$12$$10$$14$$6$ (ii) Class Interval$100–150$$150–200$$200–250$$250–300$$300– 350$$350–400$Frequency$10$$13$$17$$12$$10$$8$ Solution:-...
Draw a frequency polygon without using a histogram for the given frequency distribution:(iii)
Class Interval$1–10$$11–20$$21–30$$31–40$$41–50$Frequency$8$$12$$10$$16$$6$ Solution:- Steps to draw histograms for given frequency distributions, 1. First we have to make the class intervals...
Draw a frequency polygon without using a histogram for the given frequency distribution:(i)
Class Mark$10$$15$$20$$25$$30$$35$$40$Frequency$4$$20$$40$$45$$30$$25$$5$ (ii) Class Interval$10–20$$20–40$$40–60$$60–80$$80–100$Frequency$9$$17$$15$$20$$14$ Solution:- Steps to draw a histogram for...
Draw a histogram and then a frequency polygon for each of the following frequency distribution:(iii)
Class Interval$100–150$$150–200$$200- 250$$250–300$$300–350$Frequency$10$$15$$17$$12$$10$ Solution:- Steps to draw histograms for given frequency distributions, 1. On the x – axis, take $1cm=10$...
Draw a histogram and then a frequency polygon for each of the following frequency distribution:(i)
Class Interval$0–10$$10–20$$20–30$$30–40$$40–50$$50–60$Frequency$8$$13$$27$$35$$14$$3$ (ii) Class Interval$11–20$$21–30$$31–40$$41–50$$51–60$$61-70$Frequency$15$$28$$50$$35$$20$$12$ (i) Class...
Draw histograms for each of the following frequency distributions:(v)
Class Mark$6$$12$$18$$24$$30$$36$Frequency$8$$12$$15$$18$$25$$7$ Solution:- Steps to draw histograms for given frequency distributions, 1. First we have to calculate the class interval from the...
Draw histograms for each of the following frequency distributions:(iii)
Class Interval$1–10$$11–20$$21–30$$31–40$$41–50$Frequency$11$$23$$30$$20$$16$ Class Interval$110–119$$120–129$$130–139$$140–149$$150–159$Frequency$15$$23$$30$$20$$16$ (iii)Solution:- Steps to draw...
Draw histograms for each of the following frequency distributions:(i)
Class Interval$0–10$$10–20$$20–30$$30–40$$40–50$$50–60$Frequency$8$$20$$34$$22$$10$$6$ (ii) Class Interval$130–140$$140–150$$150–160$$160–170$$170–180$Frequency$24$$16$$29$$20$$11$ (i) Steps to draw...