The graph below shows the speed, in m/s, of a car as it comes to rest from a speed of 10 m/s. Calculate the rate at which the car is slowing down during the first three seconds.

Given: The graph below shows the speed, in m/s, of a car as it comes to rest from a speed of 10 m / s . Scale: x - a x i s 1 cm = 1 seconds y - a x i s 1 cm = 2 m / s The rate at which the car is slowing down during the first three seconds = 5 - 10 3 - 0 = - 1 . 66 m / s 2

A random survey of the number of children of various age groups playing in park was found as follows: Age(in years) Number of children 1 - 2 2 - 3 3 - 5 5 - 7 7 - 10 10 - 15 15 - 17 5 3 6 12 9 10 4 Draw a histogram to represent the data above.

The histogram is a graphical representation of a grouped frequency distribution with continuous classes. Here, the given data is having class intervals of varying width. The minimum class size is 1 . So, we need to find the proportion of children per 1 year interval as follows: Age (in years) Frequency (Number of children) Width of class Length of rectangle 1 - 2 5 1 5 × 1 1 = 5 2 - 3 3 1 3 × 1 1 = 3 3 - 5 6 2 6 × 1 2 = 3 5 - 7 12 2 12 × 1 2 = 6 7 - 10 9 3 9 × 1 3 = 3 10 - 15 10 5 10 × 1 5 = 2 15 - 17 4 2 4 × 1 2 = 2 Now taking age of children on x -axis and proportion of children per 1 year interval on y -axis (where 1 unit = 1 year on y - axis), we can draw histogram as below:

The distance-time graph represents Ibrahim's journey home to school one morning. How fast, in m/s, was Ibrahim traveling during the last 20 minutes?

Given: The distance-time graph represents Ibrahim's journey home to school one morning. Scale x - a x i s 1 c m = 10 m i n u t e s y - a x i s 1 c m = 1000 m From the graph, we can say that from 8 : 20 to till 8 : 40 , Ibrahim travelled a distance of = ( 1800 - 1200 ) m = 600 m Thus, the speed of Ibrahim was = 600 40 × 60 = 0 . 25 m / s

The graph below shows the speed, in m/s, of a car as it comes to rest from a speed of 10 m/s. Calculate the average speed of the car for this 10 second period.

Given: The graph below shows the speed, in m/s, of a car as it comes to rest from a speed of 10 m / s . Scale: x - a x i s 1 cm = 1 seconds y - a x i s 1 cm = 2 m / s average speed = area under the curve total time Area under the curve = area 1 + area 2 + area 3 = ( 1 2 × 3 × 6 ) + ( 4 × 3 ) + ( 1 2 × 7 × 4 ) = 9 + 12 + 14 = 35 m average speed = 35 10 = 3 . 5 m / s

The following table gives the lifetimes of neon lamps: Length (in hours) Number of lamps 300 - 400 400 - 500 500 - 600 600 - 700 700 - 800 800 - 900 900 - 1000 14 56 60 86 74 62 48 Represent the given information with the help of a histogram.

The histogram is a graphical representation of a grouped frequency distribution with continuous classes. By taking the lifetime (in hours) of neon lamps on x - axis and the number of lamps on y - axis where 1 unit on y - axis represents 10 lamps, we can draw the histogram of the given information as below:

The distance-time graph represents Ibrahim's journey home to school one morning. Describe the stage of Ibrahim's journey represented by the line BC.

Given: The distance-time graph represents Ibrahim's journey home to school one morning. Scale x - axis 1 cm = 10 minutes y - axis 1 cm = 1000 m From the graph, we can say that from 8 : 10 to till 8 : 20 Ibrahim was at rest.

The runs scored by two teams A and B on the first 60 balls in a cricket match are given below: Number of balls Team A Team B 1 - 6 7 - 12 13 - 18 19 - 24 25 - 30 31 - 36 37 - 42 43 - 48 49 - 54 55 - 60 2 1 8 9 4 5 6 10 6 2 5 6 2 10 5 6 3 4 8 10 Represent the data of both the teams on the same graph by frequency polygons.

Frequency polygons can also be drawn independently without drawing histograms. For this, we require the mid-points of the class-intervals used in the data. These mid-points of the class-intervals are called class-marks. We can observe from the given data that its class intervals are not continuous. There is a gap of 1 in between of them. So, we must add an adjustment factor = 1 2 = 0.5 to upper-class limits and subtract 0.5 from lower-class limits. We can find the class mark of each interval by using the formula: Class mark = upper-class limit+lower-class limit 2 Now continuous data with the class mark of each class interval can be represented as follows: Number of balls Class mark Team A Team B 0.5 - 6.5 3.5 2 5 6.5 - 12.5 9.5 1 6 12.5 - 18.5 15.5 8 2 18.5 - 24.5 21.5 9 10 24.5 - 30.5 27.5 4 5 30.5 - 36.5 33.5 5 6 36.5 - 42.5 39.5 6 3 42.5 - 48.5 45.5 10 4 48.5 - 54.5 51.5 6 8 54.5 - 60.5 57.5 2 10 Frequency polygons are used when the data is continuous and very large. It is very useful for comparing two different sets of data of the same nature, for example, comparing the performance of two different sections of the same class. Now by taking the class marks on x - axis and runs scored on y - axis (where 1 unit = 1 run on y - axis), we can construct frequency polygon as following:

The diagram below is the speed-time graph for a car journey. Calculate the acceleration during the last 10 seconds of the journey.

Given: The diagram below is the speed-time graph for a car journey. acceleration = change in velocity time taken acceleration = 0 - 20 60 - 50 = - 2 m / s 2 Thus, the acceleration in the last 10 seconds is - 2 m / s 2 .

Given below are the seats won by different political parties in the polling outcome of a state assembly election: Political Party A B C D E F Seats Won 75 55 37 29 10 37 Draw a bar graph to represent the polling results.

A bar graph is a graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. We take polling results on x - axis and the number of seats won on y - axis and choose an appropriate scale ( 1 unit = 10 seats for y - axis) so that we are able to draw the required graph of representing the given information as below:

A survey conducted by an organization for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in % ): S.No. Causes Female fatality rate ( % ) 1 . 2 . 3 . 4 . 5 . 6 . Reproductive health conditions Neuropsychiatric conditions Injuries Cardiovascular conditions Respiratory conditions Other causes 31 . 8 25 . 4 12 . 4 4 . 3 4 . 1 22 . 0 Represent the information given above graphically.

We know that, a bar graph is a graph that presents categorised data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. By representing Causes on x - axis and female fatality rate on y - axis and choosing an appropriate scale ( 1 unit = 5 % for y - axis), we can draw the bar graph as follows: All the rectangle bars are of same width and having equal spacing between them.

EASY

Earn 100

Histogram represents numerical data whereas the bar graph represents data.

50% studentsanswered this correctly

Important Questions on Statistics

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The given pie-chart depicts the expenditure incurred in $crores$ towards each sport.

Expenses (in $crores$ )

Question Image

In the given pie-chart, what is the ratio of expenditure between hockey and gymnastics?

MEDIUM

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The pie-chart represented below shows the spending by a family on various items during the year $1999$ . Study the pie-chart carefully and answer the following question:

Question Image

According to the pie-chart, the maximum amount was spent on which item?

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The pie-chart represented below shows the spending by a family on various items during the year $1999$ . Study the pie-chart carefully and answer the following question:

Question Image

The ratio of the total amount of money spent on housing to the total amount of money spent on education was

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The pie-chart represented below shows the spending by a family on various items during the year $1999$ . Study the pie-chart carefully and answer the following question:

Question Image

If the total amount spent during the year $1999$ was $₹ 46000$ , then the amount (in rupees) spent on food was

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

Write the full name of P.U.C. which is essential for vehicles.

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The pie-chart represented below shows the spending by a family on various items during the year $1999$ . Study the pie-chart carefully and answer the following question:

Question Image

If the total amount spent during the year $1999$ was $₹ 46000$ then how much money (in rupees) was spent on clothing and housing together?

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The pie-chart represented below shows the spending by a family on various items during the year $1999$ . Study the pie-chart carefully and answer the following question:

Question Image

If the total expenditure of the family for the year $1999$ was $₹ 46000$ , then the savings (in rupees) of the family was

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The given pie-chart depicts the expenditure incurred in $crores$ towards each sport.

Expenses (in $crores$ )

Question Image

In the given pie-chart, what is the difference between the expenditure incurred on cricket and football?

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The given pie-chart depicts the expenditure incurred in $crores$ towards each sport.

Expenses (in $crores$ )

Question Image

In the given pie-chart, what will be the central angle of the sector representing football?

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The graph below shows the speed, in m/s, of a car as it comes to rest from a speed of $10$ m/s.

Question Image

Calculate the rate at which the car is slowing down during the first three seconds.

HARD

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

A random survey of the number of children of various age groups playing in park was found as follows:

Age(in years)	Number of children
$1 - 2$ $2 - 3$ $3 - 5$ $5 - 7$ $7 - 10$ $10 - 15$ $15 - 17$	$5$ $3$ $6$ $12$ $9$ $10$ $4$

Draw a histogram to represent the data above.

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The distance-time graph represents Ibrahim's journey home to school one morning.

Question Image

How fast, in m/s, was Ibrahim traveling during the last 20 minutes?

MEDIUM

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The graph below shows the speed, in m/s, of a car as it comes to rest from a speed of $10$ m/s.

Question Image

Calculate the average speed of the car for this $10$ second period.

MEDIUM

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The following table gives the lifetimes of neon lamps:

Length (in hours)	Number of lamps
$300 - 400$ $400 - 500$ $500 - 600$ $600 - 700$ $700 - 800$ $800 - 900$ $900 - 1000$	$14$ $56$ $60$ $86$ $74$ $62$ $48$

Represent the given information with the help of a histogram.

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The distance-time graph represents Ibrahim's journey home to school one morning.

Question Image

Describe the stage of Ibrahim's journey represented by the line BC.

MEDIUM

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The runs scored by two teams $A$ and $B$ on the first $60$ balls in a cricket match are given below:

Number of balls	Team A	Team B
$1 - 6$ $7 - 12$ $13 - 18$ $19 - 24$ $25 - 30$ $31 - 36$ $37 - 42$ $43 - 48$ $49 - 54$ $55 - 60$	$2$ $1$ $8$ $9$ $4$ $5$ $6$ $10$ $6$ $2$	$5$ $6$ $2$ $10$ $5$ $6$ $3$ $4$ $8$ $10$

Represent the data of both the teams on the same graph by frequency polygons.

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The diagram below is the speed-time graph for a car journey.

Question Image

Calculate the acceleration during the last $10$ seconds of the journey.

MEDIUM

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

Given below are the seats won by different political parties in the polling outcome of a state assembly election:

Political Party	$A$	$B$	$C$	$D$	$E$	$F$
Seats Won	$75$	$55$	$37$	$29$	$10$	$37$

Draw a bar graph to represent the polling results.

MEDIUM

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

A survey conducted by an organization for the cause of illness and death among the women between the ages $15 - 44$ (in years) worldwide, found the following figures (in $%$ ):

S.No.	Causes	Female fatality rate ( $%$ )
$1 .$ $2 .$ $3 .$ $4 .$ $5 .$ $6 .$	Reproductive health conditions Neuropsychiatric conditions Injuries Cardiovascular conditions Respiratory conditions Other causes	$31.8$ $25.4$ $12.4$ $4.3$ $4.1$ $22.0$

Represent the information given above graphically.

EASY

Mathematics>Statistics and Probability>Statistics>Collection and Presentation of Data

The class mark of

10 - 20

Histogram represents numerical data whereas the bar graph represents data.

Important Questions on Statistics

Learn and Prepare for any exam you want !