PAGE NO 27.15:
Question 1:
The following table shows the number of patients discharged from a hospital with HIV diagnosis in different years:
Years:  2002  2003  2004  2005  2006 
Number of patients:  150  170  195  225  230 
Represent this information by a graph.
Ans:
Here, years is an independent variable and the number of patients is a dependent variable. So, we take years on the xaxis and the number of patients on the yaxis.
Let us choose the following scale:
On xaxis: 2 cm = 1 year
On yaxis: 1 cm = 10 patients
Also, let us assume that on the xaxis, origin (O) represents 2001 and on the yaxis, origin (O) represents 120, i.e. O (2001, 120).
Now, let us plot (2002, 150), (2003, 170), (2004, 195), (2005, 225), (2006, 230). These points are joined to get the graph representing the given information as shown in the figure below.
Question 2:
The following table shows the amount of rice grown by a farmer in different years:
Years:  2000  2001  2002  2003  2004  2005  2006 
Rice grown (in quintals):  200  180  240  260  250  200  270 
Plot a graph to illustrate this information.
Ans:
Here, year is an independent variable and quantity of rice grown is a dependent variable. So, we take years on the xaxis and quantity of rice grown on the yaxis.
Let us choose the following scale:
On xaxis: 2 cm = 1 year
On yaxis: 1 cm = 20 quintals
Let us assume that the origin O represents the coordinates (1999, 160).
Now, let us plot (2000, 200), (2001, 180), (2002, 240), (2003, 260), (2004, 250),(2005, 200),(2006, 270). These points are joined to get the graph representing the given information as shown in the figure below.
Question 3:
The following table gives the information regarding the number of persons employed to a piece of work and time taken to complete the work:
Number of persons:  2  4  6  8 
Time taken (in days):  12  6  4  3 
Plot a graph of this information.
Ans:
Here, number of persons is an independent variable and time taken is a dependent variable. So, we take the number of persons on the xaxis and time taken on the yaxis.
Let us choose the following scale:
On xaxis: 2 cm = 2 persons
On yaxis: 2 cm = 2 days
Now, let us plot (2, 12), (4, 6), (6, 4), (8, 3). These points are joined to get the graph representing the given information as shown in the figure below.
Question 4:
The following table gives the information regarding length of a side of a square and its area:
Length of a side (in cm):  1  2  3  4  5 
Area of square (in cm^{2}):  1  4  9  16  25 
Draw a graph to illustrate this information.
Ans:
Here, length of a side is an independent variable and area of square is a dependent variable. So, we take length of a side on the xaxis and area of square on the yaxis.
Let us choose the following scale:
On xaxis: 2 cm = 1 cm
On yaxis: 1 cm = 2 cm^{2}
Now we plot (1,1), (2,4), (3,9), (4,16), (5,25). These points are joined to get the graph representing the given information as shown in the figure below.
PAGE NO 27.16:
Question 5:
The following table shows the sales of a commodity during the years 2000 to 2006.
Years:  2000  2001  2002  2003  2004  2005  2006 
Sales (in lakhs of Rs):  1.5  1.8  2.4  3.2  5.4  7.8  8.6 
Draw a graph of this information.
Ans:
Here, year is an independent variable and sales is a dependent variable. So, we take year on the xaxis and sales on the yaxis.
Let us choose the following scale:
On xaxis: 2 cm = 1 year
On yaxis: 2 cm = 1 lakh rupees
Assume that on xaxis, origin (O) represents 1991.
So, the coordinates of O are (1991,0).
Now, let us plot (2000, 1.5), (2001, 1.8), (2002, 2.4), (2003, 3.2), (2004, 5.4), (2005, 7.8) and (2006, 8.6). These points are joined to get the graph representing the given information as shown in the figure below.
Question 6:
Draw the temperaturetime graph in each of the following cases:
(i)
Time (in hours):  7:00  9:00  11:00  13:00  15:00  17:00  19:00  21:00 
Temperature (°F) in:  100  101  104  102  100  99  100  98 
(ii)
Time (in hours):  8:00  10:00  12:00  14:00  16:00  18:00  20:00 
Temperature (°F) in:  100  101  104  103  99  98  100 
Ans:
Here, time is an independent variable and temperature is a dependent variable. So, we take time on the xaxis and temperature on the yaxis.
Let us choose the following scale:
For point (i):
On xaxis: 1 cm = 1 hours
On yaxis: 1 cm = 2^{ο}F
For point (ii):
On xaxis: 2 cm = 2 hours
On yaxis: 1 cm = 1^{ο}F
Let us assume that on the xaxis, the coordinate of origin is 6:00.
On yaxis, the coordinate of origin is 94^{ο}F .
So, the coordinates of O are (6:00, 94).
Now, let us plot (7:00, 100), (9:00, 101), (11:00, 104),..(21:00, 98) for point (i) and (8:00, 100), (10:00, 101), (12:00, 104),...,(20:00, 100) for point (ii). These points are joined to get the graphs representing the given information as shown in the figures below.
(i)
(ii)
Question 7:
Draw the velocitytime graph from the following data:
Time (in hours):  7:00  8:00  9:00  10:00  11:00  12:00  13:00  14:00 
Speed (in km/hr):  30  45  60  50  70  50  40  45 
Ans:
Here, time is an independent variable and speed is a dependent variable. So, we take time on the xaxis and speed on the yaxis.
Let us choose the following scale:
On xaxis: 2 big division = 1 hour
On yaxis: 1 big division = 10 km/hr
Let us assume that on the xaxis, the coordinate of origin (O) is 7:00.
So, the coordinates of O are (7:00,0).
Now, let us plot (7:00,30), (8:00,45), (9:00,60), (10:00,50), (11:00,70), (12:00,50), (13:00,40), (14:00,45). These points are joined to get the graph representing the given information as shown in the figure below.
Question 8:
The runs scored by a cricket team in first 15 overs are given below:
Overs:  I  II  III  IV  V  VI  VII  VIII  IX  X  XI  XII  XIII  XIV  XV 
Runs:  2  1  4  2  6  8  10  21  5  8  3  2  6  8  12 
Draw the graph representing the above data in two different ways as a graph and as a bar chart.
Ans:
Here, over is an independent variable and run is a dependent variable. So, we take overs on the xaxis and runs the on yaxis.
Let us choose the following scale:
On xaxis: 1 cm = 1 over
On yaxis: 1 cm = 2 runs
Now, let us plot (I,2), (II,1), (III,4),...,(XV,12). These points are joined to get the graph representing the given information as shown in the figure below.
Question 9:
The runs scored by two teams A and B in first 10 overs are given below:
Overs:  I  II  III  IV  V  VI  VII  VIII  IX  X 
Team A:  2  1  8  9  4  5  6  10  6  2 
Team B:  5  6  2  10  5  6  3  4  8  10 
Draw a graph depicting the data, making the graphs on the same axes in each case in two different ways as a graph and as a bar chart.
Ans:
Here, over is an independent variable and run is a dependent variable. So, we take overs on xaxis and runs on yaxis.
Let us choose the following scale:
On xaxis: 1 cm = 1 over
On yaxis: 1 cm = 1 run
Now, let us plot (I,2), (II,1), (III,8),...,(X,2) for team A and (I,5), (II,6), (III,8),....(X,10) for team B. These points are joined to get the graph representing the given information as shown in the figure below.
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