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Answer 1

Question 1:

Heights of 30 students:

155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153.

Now, let's arrange it in the ascending order.

147, 148, 148, 149, 150, 151, 152, 152, 153, 153, 153, 154, 154, 155, 155, 155, 156, 156, 157, 157, 157, 158, 158, 159, 159, 160, 160, 161, 162, 163.

With this data, let's build a frequency distribution table that includes a class interval 160 - 164, meaning the class interval is 4. (Because 164 - 160 = 4)

Hence, we will get:

$\begin{tabular}{| c | c |}\cline{1-2} \sf Class & \sf Frequency \\\cline{1-2}\sf 145 - 149 & \sf 4 \\\cline{1-2} \sf 150 - 154 &\sf 9 \\\cline{1-2} \sf 155 - 159 & \sf 12 \\\cline{1-2} \sf 160 - 164 & \sf 5 \\\cline{1-2}\end{tabular}$

But to construct a histogram, we'll need the class intervals to be continuous. For that, we'll subtract the lower limit of each class interval by 0.5, and add 0.5 to the upper limits of each of the class intervals.

$\begin{tabular}{| c | c | c |}\cline{1-3}\sf Class & \sf Adjusted Classes & \sf Frequency \\\cline{1-3}\sf 145 - 149 & \sf 144.5 - 149.5 & \sf 4 \\\cline{1-3}\sf 150 - 154 & \sf 149.5 - 154.5 & \sf 9 \\\cline{1-3}\sf 155 - 159 & \sf 154.5 - 159.5 & \sf 12 \\\cline{1-3}\sf 160 - 164 & \sf 159.5 - 164.5 & \sf 5 \\\cline{1-3}\end{tabular}$

[Check attachment 1 for the histogram]

Question 2:

Marks obtained by 35 students.

66, 71, 58, 81, 66, 71, 48, 69, 69, 66, 83, 73, 83, 69, 64, 69, 48, 84, 66, 58, 58, 60, 64, 66, 71, 84, 69, 64, 73, 48, 64, 69, 85, 89, 80.

Now, let's arrange it in the ascending order.

48, 48, 48, 58, 58, 58, 60, 64, 64, 64, 64, 66, 66, 66, 66, 66, 69, 69, 69, 69, 69, 69, 71, 71, 71, 73, 73, 80, 81, 83, 83, 84, 84, 85, 89.

With this data, let's build a frequency distribution table that includes a class interval 70 - 80, meaning the class interval is 10. (Because 80 - 70 = 10)

$\begin{tabular}{| c | c |}\cline{1-2} \sf Class & \sf Frequency \\\cline{1-2}\sf 48 - 58 & \sf 6 \\\cline{1-2} \sf 59 - 69 &\sf 16 \\\cline{1-2} \sf 70 - 80 & \sf 6 \\\cline{1-2} \sf 81 - 91 & \sf 7 \\\cline{1-2}\end{tabular}$

But to construct a histogram, we'll need the class intervals to be continuous. For that, we'll subtract the lower limit of each class interval by 0.5, and add 0.5 to the upper limits of each of the class intervals.

$\begin{tabular}{| c | c | c |}\cline{1-3}\sf Class & \sf Adjusted Classes & \sf Frequency \\\cline{1-3}\sf 48 - 58 & \sf 47.5 - 58.5 & \sf 6 \\\cline{1-3}\sf 59 - 69 & \sf 58.5 - 69.5 & \sf 16 \\\cline{1-3}\sf 70 - 80 & \sf 69.5 - 80.5 & \sf 6 \\\cline{1-3}\sf 81 - 91 & \sf 80.5 - 91.5 & \sf 7 \\\cline{1-3}\end{tabular}$

[Check attachment 2 for the histogram]

Scale for Histogram 1:

x-axis: 2 units = 5 cms.

y-axis: 1 unit = 2 cms.

Scale for Histogram 2:

x-axis: 2 units = 11cms.

y-axis: 1 unit = 2 cms.

Answer 2

$\sf\orange{ QUESTION 1 :- }$

The heights (in cm) of 30 students of class VIII are given below:

155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153.

Prepare a frequency distribution table with 160-164 as one of the class intervals. Draw a graph(Histogram) to illustrate it.

$\sf\blue{ ANSWER :- }$

Ascending order -

147 , 148 , 148 , 149 , 150 , 151 , 152 , 152 , 153 , 153 , 153 , 154 , 154 , 155 , 155 , 155 , 156 , 156 , 157 , 157 , 157 , 158 , 158 , 159 , 159 , 160 , 160 , 161 , 162 , 163

The largest height = 163

The smallest height = 147

Range = 163 - 147 = 16

Class size = 164 - 160 = 4

Since 16/4 = 4 , so we have 4 class interval each of size 5.

the classes of equal size covering the given data are → 144 - 148 , 148 - 152 , 152 - 156 , 156 - 160 , 160 -164

FREQUENCY DISTRIBUTION TABLE

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf marks &\sf Tally \: marks&\sf frequency \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 144 - 148& \sf{l} &\sf 1 \\\\\sf 148 - 152 &\sf \cancel{llll} &\sf 5 \\\\\sf 152 - 156&\sf \cancel{llll} \:\cancel{llll} &\sf 10 \\\\\sf 156 - 160&\sf \cancel{llll} \: llll&\sf 9\\\\\sf 160 - 164&\sf \cancel{llll} &\sf 5 \\\\\sf Total &\sf &\sf 30\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{\bf{}}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\end{array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

HISTOGRAM

[ IN FIRST ATTACHMENT]

__________________________________________

$\sf\orange{ QUESTION 2 :- }$

Following are the marks obtained in Mathematics by 35 students. Prepare a frequency distribution table with one of the classes as 70-80. Draw a graph(Histogram) to illustrate it.

66, 71, 58, 81, 66, 71, 48, 69, 69, 66, 83, 73, 83, 69, 64, 69, 48, 84, 66, 58, 58, 60, 64, 66, 71, 84, 69, 64, 73, 48, 64, 69, 85, 89, 80

$\sf\orange{ ANSWER :- }$

Ascending order:-

48, 48, 48, 58, 58, 58, 60, 64, 64, 64, 64, 66, 66, 66, 66, 66, 69, 69, 69, 69, 69, 69, 71, 71, 71, 73, 73, 80, 81, 83, 83, 84, 84, 85, 89

The highest marks = 89

The lowest marks = 48

Range = 89 - 48 = 41

Class size = 80 - 70 = 10

the classes of equal size covering the given data are → 40 - 50 , 50 - 60 , 60 - 70 , 70 - 80 , 80 - 90

FREQUENCY DISTRIBUTION TABLE

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf marks &\sf Tally \: marks&\sf frequency \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 40 - 50&\sf {lll} &\sf 3 \\\\\sf 50 - 60 &\sf {lll} &\sf 3 \\\\\sf 60 - 70&\sf \cancel{llll} \:\cancel{llll} \:\cancel{llll} \:l&\sf 16 \\\\\sf 70 - 80&\sf \cancel{llll}&\sf 5\\\\\sf 80 - 90&\sf \cancel{llll} \: lll &\sf 8 \\\\\sf Total &\sf &\sf 35\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{\bf{}}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\end{array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

HISTOGRAM

[ IN SECOND ATTACHMENT]