Define statistics as a subject.

Define some fundamental characteristics of statistics.

What are primary data and secondary data? Which of the two is more reliable and why?

Explain the meaning of each of the following terms:

(i) Variate

(ii) Class interval

(iii) Class size

(iv) Class mark

(v) Class limit

(vi) True class limits

(vii) Frequency of a class

(viii) Cumulative frequency of a class

Following data gives the number of children in 40 families:

1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.

Represent it in the form of a frequency distribution, taking classes 0-2, 1-4, etc.

The marks obtained by 40 students of a class in an examination are given below.

3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 24, 6, 23, 15.

Present the data in the form of a frequency distribution using equal class size, one such class being 10 – 15 (15 not included).

Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.

18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17, 15, 6, 18, 23, 22, 16, 9, 21, 11, 16.

Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210-230 (230 not included).

220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

The weights (in grams) of 40 oranges picked at random from a basket are as follows:

40, 50, 60, 65, 45, 55, 30, 90, 75, 85, 75, 80, 100, 110, 70, 55, 30, 35, 45, 70, 80, 85, 95, 70, 60, 70, 75, 40, 100, 65, 60, 40, 100, 75, 110, 30, 45, 84.

Construct a frequency table as well as a cumulative frequency table.

The weekly wages (in rupees) of 30 workers in a factory are given below: 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.

Represent the data in the form of a frequency distribution with class size 10.

The electricity bills (in rupees) of 40 houses in a locality are given below:

116, 127, 107, 100, 80, 82, 91, 101, 65, 95, 87, 81, 105, 129, 92, 75, 89, 78, 87, 81, 59, 52, 65, 101, 115, 108, 95, 65, 98, 62, 84, 76, 63, 128, 121, 61, 118, 108, 116, 130.

Construct a grouped frequency table.

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

Construct the cumulative frequency table for the above data.

Present the following as an ordinary grouped frequency table:

Given below is a cumulative frequency table:

Extract a frequency table from the above.

Make a frequency table from the following:

The following table shows the number of students participating in various in a school.

Draw a bar graph to represent the above data.

On a certain day, the temperature in a city was recorded as under:

Illustrate the data by a bar graph.

The approximate velocities of some vehicles are given below:

Draw a bar graph to represent the above data.

The following table shows the favorite sports of 250 students of a school. Represent the data by a bar graph.

Given below is a table which shows the year wise strength of a school. Represent this data by a bar graph.

The following table shows the number of scooters produced by a company during six consecutive years. Draw a bar graph to represent this data.

The birth rate per thousand in five countries over a period of time is shown below:

Represent the above data by a bar graph.

The following table shows the interest paid by India (in thousand crore rupees) on external debts during the period 1998-99 to 2002-03. Represent the data by a bar graph.

The air distances of four cities from Delhi (in km) are given below:

Draw a bar graph to represent the above data.

The following table shows the life expectancy (average age to which people live) in various countries in a particular year.

Represent this data by a bar graph.

Gold prices on 4 consecutive Tuesdays were as under:

Draw a bar graph to show this information.

Various modes of transport used by 1850 students of a school are given below.

Draw a bar graph to represent the above data.

Look at the bar graph given below.

Bar Graph Showing the marks obtained by a student in an examination

Read it carefully and answer the following questions.

(i) What information does the bar graph give?

(ii) In which subject is the student very good?

(iii) In which subject is he poor?

(iv) What is the average of his marks?

The daily wages of 50 workers in a factory are given below:

Construct a histogram to represent the above frequency distribution.

The following table shows the average daily earnings of 40 general stores in a market, during a certain week.

Draw a histogram to represent the above data.

The heights of 75 students in a school are given below:

Draw a histogram to represent the above data.

Draw a histogram for the frequency distribution of the following data.

Construct a histogram for the following frequency distribution.

The following table shows the number of illiterate persons in the age group (10-58 years) in a town:

Draw a histogram to represent the above data.

Draw a histogram to represent the following data.

In a study of diabetic patients in a village, the following observations were noted.

Represent the above data by a frequency polygon.

The ages (in years) of 360 patience treated in a hospital on a particular day are given below.

Draw a histogram and a frequency polygon on the same graph to represent the above data.

Draw a histogram and the frequency polygon from the following data.

Draw a histogram for the following data:

Using this histogram, draw the frequency polygon on the same graph.

Draw a frequency polygon for the following frequency distribution.

Find the arithmetic mean of

(i) the first eight natural numbers

(ii) the first ten odd numbers

(iii) the first five prime numbers

(iv) the first six even numbers

(v) the first seven multiples of 5

(vi) all the factors of 20

The number of children in 10 families of a locality are

2, 4, 3, 4, 2, 0, 3, 5, 1, 6.

Find the mean number of children per family.

The following are the number of books issued in a school library during a week:

105, 216, 322, 167, 273, 405 and 346.

Find the average number of books issued per day.

The daily minimum temperature recorded (in degree F) at a place during a week was as under:

Find the mean temperature.

The percentage of marks obtained by 12 students of a class in mathematics are

64, 36, 47, 23, 0, 19, 81, 93, 72, 35, 3, 1.

Find the mean percentage of marks.

If the arithmetic mean of 7, 9, 11, 13, x, 21 is 13, find the value of x.

The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean?

The mean of 20 numbers is 43. If 6 is subtracted from each of the numbers, what will be the new mean?

The man of 15 numbers is 27. If each number is multiplied by 4, what will be the mean of the new numbers?

The mean of 12 numbers is 40. If each number is divided by 8, what will be the mean of the new numbers?

The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers, find the mean of the new set of 20 numbers.

The mean weight of 6 boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg. Find the weight of the sixth boy.

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. Find the correct mean.

The mean of 100 items was found to be 64. Later on it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. Find the correct mean.

The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.

The mean mark obtained by 7 students in a group is 226. If the marks obtained by six of them are 340, 180, 260, 56, 275 and 307 respectively, find the marks obtained by the seventh student.

The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean rises by 500 g. Find the weight of the teacher.

The mean weight of a class of 36 students is 41 kg. If one of the students leaves the class then the mean is decreased by 200 g. Find the weight of the student who left.

The average weight of a class of 39 students is 40 kg. When a new student is admitted to the class, the average decreases by 200 g. Find the weight of the new student.

The average monthly salary of 20 workers in an office is ₹ 7650. if the manager’s salary is added, the average salary becomes ₹ 8200 per month. What is the manager’s salary per month?

The average monthly wage of a group of 10 persons is ₹ 9000. One member of the group, whose monthly wage is ₹ 8100, leaves the group and is replaced by a new member whose monthly wage is ₹ 7200. Find the new monthly average wage.

The average monthly consumption of petrol for a car for the first 7 months of a year is 330 litres, and for the next 5 months is 270 liters. What is the average consumption per month during the whole year?

Find the mean of 25 numbers if the mean of 15 of them is 18 and the mean of the remaining numbers is 13.

The mean weight of 60 students of a class is 52.75 kg. If the mean weight of 25 of them is 51 kg, find the mean weight of the remaining students.

The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weights 58 kg is replaced by a new man. Find the weight of the new man.

The mean of 8 numbers is 35. If a number is excluded then the mean is reduced by 3. Find the excluded number.

The mean of 150 items was found to be 60. Later on, it was discovered that the values of two items were misread as 52 and 8 instead of 152 and 88 respectively. Find the correct mean.

The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16^th results.

The mean of 11 numbers is 42. If the mean of the first 6 numbers is 37 and that of the last 6 numbers is 46, find the 6^th number.

The mean weight of 25 students of a class is 52 kg. If the mean weight of the first 13 students of the class is 48 kg and that of the last 13 students is 55 kg. find the weight of the 13^th student.

The mean score of 25 observations is 80 and the mean score of another 55 observations is 60. Determine the mean score of the whole set of observations.

Arun scored 36 marks in English, 44 marks in Hindi, 75 marks in mathematics and x marks in science. If he has secured an average of 50 marks, find the value of x.

The mean monthly salary paid to 75 workers in a factory is ₹ 5680. The mean salary of 25 of them is ₹ 5400 and that of 30 others is ₹ 5700. Find the mean salary of the remaining workers.

A ship sails out to an island at the rate of 15 km/h and sails back to the starting point at 10 km/h. Find the average sailing speed for the whole journey.

There are 50 students in a class, of which 40 are boys. The average weight of the class is 44 kg and that the girls is 40 kg. Find the average weight of the boys.

Find the mean of daily wages of 60 workers in a factory as per data given below:

The following table shows the weights of 12 workers in a factory.

Find the mean weight of the workers.

The following data give the number of boys of a particular age in a class of 40 students.

Calculate the mean age of the students.

Find the mean of the following frequency distribution:

If the mean of the following frequency distribution is 8, find the value of p.

Find the missing frequency p for the following frequency distribution whose mean is 28.25.

Find the value of p for the following frequency distribution whose mean is 16.6.

Find the missing frequencies in the following frequency distribution, whose mean is 50.

Use the assumed-mean method to find the mean weekly wages from the data given below.

Use the assumed-mean method to find the mean height of the plants from the following frequency-distribution table.

Use the step-deviation method to find the arithmetic mean from the following data.

The table given below gives the distribution of villages and their heights from the sea level in a certain region.

Compute the mean height, using the step-deviation method.

Find the median of

(i) 2, 10, 9, 9, 5, 2, 3, 7, 11

(ii) 15, 6, 16, 8, 22, 21, 9, 18, 25

(iii) 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22

(iv) 7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2

Find the median of

(i) 17, 19, 32, 10, 22, 21, 9, 35

(ii) 72, 63, 29, 51, 35, 60, 55, 91, 85, 82

(iii) 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17, 27

The marks of 15 students in an examination are:

25, 19, 17, 24, 23, 29, 31, 40, 19, 20, 22, 26, 17, 35, 21.

Find the median score.

The heights (in cm) of 9 girls are:

144.2, 148.5, 143.7, 149.6, 150, 146.5, 145, 147.3, 152.1.

Find the median height.

The weights (in kg) of 8 children are:

13.4, 10.6, 12.7, 17.2, 14.3, 15, 16.5, 9.8.

Find the median weight.

The ages (in years) of 10 teachers in a school are:

32, 44, 53, 47, 37, 54, 34, 36, 40, 50.

Find the median age.

If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are ten observations in an ascending order with median 24, find the value of x.

Find the median weight for the following data.

Find the median for the following frequency distribution.

Calculate the median for the following data.

The heights (in cm) of 50 students of a class are given below:

Find the median for the following height.

Find the median for the following data:

Find the mode of the following items.

0, 6, 5, 1, 6, 4, 3, 0, 2, 6, 5, 6

Determine the mode of the following values of variables.

23, 15, 25, 40, 27, 25, 22, 25, 20

Calculate the mode of the following sizes of shoes sold by a shop on a particular day.

5, 9, 8, 6, 9, 4, 3, 9, 1, 6, 3, 9, 7, 1, 2, 5, 9

A cricket player scored the following runs in 12 one-day matches:

50, 30, 9, 32, 60, 50, 28, 50, 19, 50, 27, 35.

Find his modal score.

Calculate the mode of each of the following using the empirical formula.

17, 10, 12, 11, 10, 15, 14, 11, 12, 13

The table given below shows the weights (in kg) of 50 persons:

Find the mean, median and mode.

The marks obtained by 80 students in a test are given below:

Find the modal marks.

The ages of the employees of a company are given below:

Find the mean, median and mode for the above data.

The following table shows the weights of 12 students.

The range of the data

12, 25, 15, 18, 17, 20, 22, 6, 16, 11, 8, 19, 10, 30, 20, 32 is

The class mark of the class 100-120 is

In the class intervals 10-20, 20-30, the number 20 is included in

The class marks of a frequency distribution are 15, 20, 25, 30…..

The class corresponding to the class mark 20 is

In a frequency distribution, the mild-value of a class is 10 and width of each class is 6. The lower limit of the class is

Let m be the midpoint and u be the upper class limit of a class in a continuous distribution. The lower class limit of the class is

The width of each of the five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is

Let L be the lower class boundary of a class in a frequency distribution and m be the midpoint of the class. Which one of the following is the upper class boundary of the class?

The mid-value of a class interval is 42 and the class size is 10. The lower and upper limits are

If the mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is

If the mean of x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observation is

If each observation of a data is increased by 5, then their mean

Let be the mean of x₁, x₂, …., x_n and be the mean of y₁, y₂, …y_n. If is the mean of x₁, x₂, …., x_n, y₁, y₂…, y_n, then = ?

If is the mean of x₁, x₂, …, x_n then for a ≠ 0, the mean of

If are the means of n groups with number of observations respectively, then the mean of all the groups taken together is

The mean weight of six boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 46kg and 44 kg. The weight of the 6^th boy is

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. The correct mean is

The mean of 100 items was found to be 64. Later on it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. the correct mean is

The mean of 100 observations is 50. If one of the observations 50 is replaced by 150, the resulting mean will be

The mean of 25 observations is 36. Out of these observations, the mean of first 13 is 32 and that of the last 13 is 40. The 13^th observation is

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be -3.5. The mean of the given numbers is

The mean of the following data is 8.

The value of p is

The runs scored by 11 members of a cricket team are

15, 34, 56, 27, 43, 29, 31, 13, 50, 20, 0

The median score is

The weight of 10 students (in kgs) are

55, 40, 35, 52, 60, 38, 36, 45, 31, 44

The median weight is

The median of the numbers 4, 4, 5, 7, 6, 7, 7, 12, 3 is

The median of the numbers 84, 78, 54, 56, 68, 22, 34, 45, 39, 54 is

Mode of the data 15, 17, 15, 19, 14, 18, 15, 14, 16, 15, 14, 20, 19, 14, 15 is

For drawing a frequency polygon of a continuous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abscissa are respectively

The marks obtained by 17 students of a class in a test (out of 100) are given below:

90, 79, 76, 82, 46, 64, 72, 49, 68, 66, 48, 91, 82, 100, 96, 65, 84

The range data is

The class mark of the class 130-150 is

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is

The median of the data arranged in ascending order 8, 9, 12, 18, (x + 2), (x + 4), 30, 31, 34, 39 is 24. The value of x is

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

The mode of the data 2, 3, 9, 16, 9, 3, 9 is 16.

The median of 3, 14, 18, 20, 5 is 18.

The median of 1, 3, 2, 5, 8, 6, 1, 4, 7, 9 = (5^th term + 6^th term)

Match the following column.

The correct answer is:

(a)-……., (b)-……., (c)-……., (d)-…….,

The class marks of a frequency distribution are 47, 52, 57, 62, 67, 72, 77. Determine the (i) class size (ii) class limits with respect to the class mark 52 (iii) true class limits for class mark 52.

Which is false?

Which is false?

Which is false?

Look at the table given below:

The true lower limit of the class 21-30 is

Look at the table given below:

The true upper limit of the class 10-20 is

Look at the table given below:

What is the class size of the class 11-20 in this table?

What is the class mark of class 21-30 in the table of Q.3 ?

If the mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 11, find the value of x.

The points scored by a kabaddi team in a series of matches are as follows:

8, 24, 10, 14, 5, 15, 7, 2, 17, 27, 10, 7, 48, 8, 18, 28

Find the median of the points scored by a team.

The following table shows the number of students participating in the various games in a school:

Draw a bar graph to represent the above data.

The heights of five players are 148 cm, 154 cm, 153 cm, 140 cm, and 150 cm, respectively. Find the mean height per player.

The marks obtained by 12 students of a class in the test are:

36, 27, 5, 19, 34, 23, 37, 23, 16, 23, 20, 38

The class marks of a frequency distribution are

26, 31, 36, 41, 46, 51

Find the true class limits.

The mean of the following frequency distribution is 8. Find the value of p.

If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are ten observations in an ascending order with median 24, Find the value of x.

Calculate the mode of the following using empirical formula:

17, 10, 12, 11, 10, 15, 14, 11, 12, 13

Find the medium of the following frequency distribution:

The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.

Fill in the blanks in the following table:

In the city, the weekly observations made on the cost of living index are given below.

Represent the above information in the form of a histogram.

The mean of the marks scored by 50 students was found to be 39, Later on, it was discovered that a score was 43 was misread as 23, Find the correct mean.

The following table shows the weights of 12 workers in the factory.

Find the mean weight of the workers.

The heights (in cm) of 50 students of class are given below.

Find the median height