NCERT Exemplar Solutions
Class 7 - Mathematics

Unit 3: Data Handling

The difference between the highest and the lowest observations of a data is called ________.

The mean of a data is defined as ________.

In a set of observations, the observation that occurs the most often is called ________.

In a given data, arranged in ascending or descending order, the middle most observation is called ________.

Mean, Median, Mode are the measures of ________.

The probability of an event which is certain to happen is ________.

The probability of an event which is impossible to happen is ________.

When a die is thrown, the probability of getting a number less than 7 is ________.

In throwing a die the number of possible outcomes is ________.

________ can be used to compare two collections of data.

The representation of data with bars of uniform width is called ________.

If the arithmetic mean of 8, 4, x, 6, 2, 7 is 5, then the value of x is ________.

The median of any data lies between the ________ and ________ observations.

Median is one of the observations in the data if number of observations is ________.

Rohit collected the data regarding weights of students of his class and prepared the following table:

A student is to be selected randomly from his class for some competition. The probability of selection of the student is highest whose weight is in the interval ________.

If a die is thrown, the probability of getting a number greater than 6 is 1.

When a coin is tossed, there are 2 possible outcomes.

If the extreme observations on both the ends of a data arranged in ascending order are removed, the median gets affected.

The measures of central tendency may not lie between the maximum and minimum values of data.

It is impossible to get a sum of 14 of the numbers on both dice when a pair of dice is thrown together.

The probability of the spinning arrow stopping in the shaded region (Fig. 3.4) is \(\dfrac{1}{2}\).

A coin is tossed 15 times and the outcomes are recorded as follows: H T T H T H H H T T H T H T T. The chance of occurrence of a head is 50 per cent.

Mean, Median and Mode may be the same for some data.

The probability of getting an ace out of a deck of cards is greater than 1.

Mean of the data is always from the given data.

Median of the data may or may not be from the given data.

Mode of the data is always from the given data.

Mean of the observations can be lesser than each of the observations.

Mean can never be a fraction.

Range of the data is always from the data.

The data 12, 13, 14, 15, 16 has every observation as mode.

The range of the data 2, −5, 4, 3, 7, 6 would change if 2 was subtracted from each value in the data.

The range of the data 3, 7, 1, −2, 2, 6, −3, −5 would change if 8 was added to each value in the data.

Calculate the Mean, Median and Mode of the following data: 5, 10, 10, 12, 13.
Are these three equal?

Find the mean of the first ten even natural numbers.

A data constitutes of heights (in cm) of 50 children. What do you understand by mode for the data?

A car seller collects the following data of cars sold in his shop:

(a) Which colour of the car is most liked?
(b) Which measure of central tendency was used in (a)?

The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29.
For the given data, find the
(a) Range (b) Mean (c) Median (d) Mode

The following are weights (in kg) of 12 people: 70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78, 60.
(a) Find the mean of the weights of the people.
(b) How many people weigh above the mean weight?
(c) Find the range of the given data.

Following cards are put facing down: A, E, I, O, U. What is the chance of drawing out
(a) a vowel
(b) A or I
(c) a card marked U
(d) a consonant

For the given data calculate the mean of its median and mode: 6, 2, 5, 4, 3, 4, 4, 2, 3.

Find the median of the given data if the mean is 4.5: 5, 7, 7, 8, x, 5, 4, 3, 1, 2.

What is the probability of the sun setting tomorrow?

When a spinner with three colours (Fig. 3.5) is rotated, which colour has more chance to show up with arrow than the others?

What is the probability that a student chosen at random out of 3 girls and 4 boys is a boy?

The letters written on paper slips of the word MEDIAN are put in a bag. If one slip is drawn randomly, what is the probability that it bears the letter D?

Classify the following events as certain to happen, impossible to happen, may or may not happen:
(a) Getting a number less than 1 on throwing a die.
(b) Getting head when a coin is tossed.
(c) A team winning the match.
(d) Christmas will be on 25 December.
(e) Today moon will not revolve around the earth.
(f) A ball thrown up in the air will fall down after some time.

A die was thrown 15 times and the outcomes recorded were 5, 3, 4, 1, 2, 6, 4, 2, 2, 3, 1, 5, 6, 1, 2. Find the mean, median and mode of the data.

Find the mean of first six multiples of 4.

Find the median of first nine even natural numbers.

The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers.

Find the mode of the given data: 10, 8, 4, 7, 8, 11, 15, 8, 4, 2, 3, 6, 8.

Heights of 15 boys (in cm): 128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.
Find (a) The height of the tallest boy.
(b) The height of the shortest boy.
(c) The range of the given data.
(d) The median height of the boys.

Observe the data and answer:
16, 15, 16, 16, 8, 15, 17
(a) Which data value can be put in the data so that the mode remains the same?
(b) At least how many and which value(s) must be put in to change the mode to 15?
(c) What is the least number of data values that must be put in to change the mode to 17? Name them.

Ages (in years) of 6 children of two groups are recorded as below:

(a) Find the mode and range for each group.
(b) Find the range and mode if the two groups are combined together.

Observe the given bar graph carefully and answer the questions that follow.

(a) What information does the bar graph depict?
(b) How many motor bikes were produced in the first three months?
(c) Calculate the increase in production in May over the production in January.
(d) In which month the production was minimum and what was it?
(e) Calculate the average (mean) production of bikes in 6 months.

The bar graph given below shows the marks of students of a class in a particular subject:

(a) If 40 is the pass mark, then how many students have failed?
(b) How many students got marks from 50 to 69?
(c) How many students scored 90 marks and above?
(d) If students who scored marks above 80 are given merits then how many merit holders are there?
(e) What is the strength of the class?

Study the bar graph given below and answer the questions that follow.

(a) What information does the above bar graph represent?
(b) In which year was production the least?
(c) After which year was the maximum rise in the production?
(d) Find the average production of rice during the 5 years.
(e) Find difference of rice production between years 2006 and 2008.

Study the bar graph given below and answer the questions that follow:

(a) What information is depicted from the bar graph?
(b) In which subject is the student very good?
(c) Calculate the average marks of the student.
(d) If 75 and above marks denote a distinction, then name the subjects in which the student got distinction.
(e) Calculate the percentage of marks the student got out of 500.

The bar graph given below represents the circulation of newspapers (dailies) in a town in six languages (figures approx. to hundreds).

(a) Find the total number of newspapers read in Hindi, Punjabi, Urdu, Marathi and Tamil.
(b) Find the excess number of newspapers read in Hindi than those in English.
(c) Name the language in which the least number of newspapers are read.
(d) Write the total circulation of newspapers in the town.

Study the double bar graphs given below and answer the following questions:

(a) Which sport is liked the most by Class VIII students?
(b) How many students of Class VII like Hockey and Tennis in all?
(c) How many students are there in Class VII?
(d) For which sport is the number of students of Class VII less than that of Class VIII?
(e) For how many sports students of Class VIII are less than Class VII?
(f) Find the ratio of students who like Badminton in Class VII to students who like Tennis in Class VIII.

Study the double bar graph shown below and answer the questions that follow:

(a) What information is represented by the above double bar graph?
(b) In which month sales of Brand A decreased as compared to the previous month?
(c) What is the difference in sales of both the Brands for the month of June?
(d) Find the average sales of Brand B for the six months.
(e) List all months for which the sales of Brand B was less than that of Brand A.
(f) Find the ratio of sales of Brand A as compared to Brand B for the month of January.

Study the double bar graph given below and answer the questions that follow:

(a) What information is compared in the above given double bar graph?
(b) Calculate the ratio of minimum temperatures in the year 2008 to the year 2009 for the month of November.
(c) For how many months was the minimum temperature in the year 2008 greater than that of year 2009? Name those months.
(d) Find the average minimum temperature for the year 2008 for the four months.
(e) In which month is the variation in the two temperatures maximum?

The following table shows the average intake of nutrients in calories by rural and urban groups in a particular year. Using a suitable scale for the given data, draw a double bar graph to compare the data.

Study the double bar graph and answer the questions that follow:

(a) What information does the double bar graph represent?
(b) Find the total number of boys in all sections of Class VII.
(c) In which sections, the number of girls is greater than the number of boys?
(d) In which section, the number of boys is the maximum?
(e) In which section, the number of girls is the least?

In a public library, the following observations were recorded by the librarian in a particular week:

(a) Draw a double bar graph choosing an appropriate scale.
(b) On which day, the number of readers in the library was maximum?
(c) What is the mean number of magazine readers?

Observe the following data:

(a) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(b) Which class has the maximum number of students?
(c) In which class, the difference of total students and number of students present is minimum?
(d) Find the ratio of number of students present to the total number of students of Class IX.
(e) What per cent of Class VI students were absent?

Observe the given data:

(a) Draw a bar graph to represent the above given information.
(b) On which day of the week was the sales maximum?
(c) Find the total sales during the week.
(d) Find the ratio of the minimum sale to the maximum sale.
(e) Calculate the average sale during the week.
(f) On how many days of the week was the sale above the average sales?

Below is a list of 10 tallest buildings in India...

(a) Find the height of each storey of the three tallest buildings and write them.
(b) The average height of one storey for the buildings given in (a).
(c) Which city in this list has the largest percentage of skyscrapers?
(d) What is the range of data?
(e) Find the median of the data.
(f) Draw a bar graph for given data.

The marks out of 100 obtained by Kunal and Soni...

The students of Class VII have to choose one club...

The data given below shows the production of motor bikes...

The table below compares the population...

The table below gives the data of tourists visiting 5 hill stations...

The table below gives the flavours of ice cream liked by children...