Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 21 - Measures of central tendency [Latest edition]

Calculate the arithmetic mean of 5.6, 6.6, 7.2, 9.3, 6.2.

The weight (in kg) of 8 new born babies are 3, 3.2, 3.4, 3.5, 4, 3.6, 4.1, 3.2. Find their A.M.

The mean of 9 variates is 11. If eight of them are 7, 12, 9, 14, 21, 3, 8 and 15, find the 9th variate.

In a class test, the mean marks scored by a class of 40 students was calculated as 18.2. Later on, it was detected that the marks of one student was wrongly copied as 21 instead of 29. Find the correct mean.

The average marks scored by the students of a class in mathematics is 75. The average of marks scored by boys and girls are respectively 79 and 59. Find the percentage of boys in the class.

Find the mean by direct method:

Find the mean by short-cut method:

Find the mean by step deviation method:

Find the average age from the following distribution:

Find the mean by step deviation method:

Find the mean:

If the mean of the following distribution is 6, find the value of p.

The mean of the following frequency distribution is 57.6 and the sum of observations is 50. Find the values of f₁ and f₂.

If the mean of the following distribution is 24, find the value of m.

Calculate the mean of the following frequency distribution:

The mean of the following distribution is 50. Find the unknown frequency:

The mean of the following data is 16. Calculate the value of f:

The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method.  Take the assumed mean as 45. Give your answer correct to 2 decimal places.

Calculate the mean of the following distribution using step deviation method:

The following table gives the duration of movies in minutes:

Using step-deviation method, find the mean duration of the movies.

Find the median of the following data:

25, 18, 16, 9, 11, 17, 29, 35, 6

Find the median of the given values:

31, 38, 27, 28, 36, 25, 35, 40

For the following set of numbers, find the median:

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

Following numbers are arrange in ascending order: 11, 13, 15, 19, х + 2, x + 4, 30, 35, 39, 46. Their median is 25. Find the value of x.

The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3. Find the median of the scores.

Find the median of the following distribution:

Calculate the median of the following frequency distribution:

In a class test, the marks scored by 18 students are 31, 53, 42, 25, 30, 26, 45, 38, 41, 35, 29, 47, 35, 28, 29, 23, 31, 21. Find:

1. lower quartile 
2. upper quartile 
3. interquartile range.

For the following frequency distribution, find:

1. lower quartile 
2. upper quartile 
3. interquartile range

For the following frequency distribution, find:

1. median 
2. lower quartile
3. upper quartile 
4. interquartile range

Find the mean, median and mode of the following data: 

10, 13, 6, 11, 10, 6, 7, 10, 8

Find the mode of the following data:

15, 14, 19, 20, 14, 15, 16, 15, 16, 18, 14, 19, 15, 17, 15

Find the value of K for which the mode of the following data is 7. 

3, 5, 5, 7, 3, 6, 7, 9, 6, 7, 3, 5, 7, 3, К

The demand of different shirt sizes, as obtained by a survey, is given below:

Find the modal shirt sizes as observed from the survey.

Find the median and mode:

Find the mean and modal class:

Draw a histogram for the following frequency distribution and find the mode from the graph.

The daily wages (in rupees) of 30 employees in an establishment are distributed as follows:

Estimate the modal daily wages for this distribution by drawing a histogram.

Find the value of mode from the following frequency distribution.

Find the mode for the following distribution: 

Find the mode of the following distribution.

Calculate the mode from the following data: 

Find the modal height of the following distribution by drawing a histogram:

A Mathematics aptitude test of 50 students was recorded as follows:

Draw a histogram for the above data using a graph paper and locate the mode.

Draw a histogram and estimate the mode for the following frequency distribution:

Draw a histogram for the following distribution:

Find the mode from the following:

Using a graph paper draw a histogram of the given distribution showing the number of runs scored by 50 batsmen. Estimate the mode of the data:

The given graph with a histogram represents the number of plants of different heights grown in a school campus. Study the graph carefully and answer the following questions:

1. Make a frequency table with respect to the class boundaries and their corresponding frequencies.
2. State the modal class.
3. Identify and note down the mode of the distribution.
4. Find the number of plants whose height range is between 80 cm to 90 cm.

Marks obtained by 40 students in an examination are given below:

Using graph paper, draw an ogive and estimate the median marks.

40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below:

Use a graph paper to draw an ogive for the above distribution.

Use a scale of 2 cm = 1 m on one axis and 2 cm = 5 students on the other axis.

Hence, using your graph, find:

1. the median. 
2. upper quartile.
3. number of students who cover a distance which is above `16 1/2` m.

Use Graph paper for this question.

A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded:

Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other axis draw an ogive of the above distribution. Use the graph to estimate the following:

1. the median
2. lower quartile
3. if above 158 cm is considered as the tall boys of the class. Find the number of boys in the class who are tall.

The daily wages of 80 workers in a project are given below.

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1. the median wage of the workers.
2. the lower quartile wage of workers.
3. the numbers of workers who earn more than Rs. 625 daily.

Marks obtained by 200 students in an examination are given below:

Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

1. The median marks.
2. The number of students who failed if minimum marks required to pass is 40.
3. If scoring 85 and more marks are considered as grade one, find the number of students who secured grade one in the examination.

The marks obtained by 120 students in a Mathematics test are given below:

Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for ogive to estimate the following:

1. The median.
2. The number of students who obtained more than 75% marks in the test.
3. The number of students who did not pass in the test if the pass percentage was 40.

The following distribution represents the height of 160 students of a school.

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

1. The median height.
2. The inter quartile range.
3. The number of students whose height is above 172 cm.

The daily wages of 160 workers in a building project are given below:

Using a graph paper, draw an Ogive for the above distribution. Use your Ogive to estimate:

1. the median wage of the workers.
2. the upper quartile wage of the workers.
3. the lower quartile wages of the workers.
4. the percentage of workers who earn more than ₹ 45 a day.

The monthly income of a group of 320 employees in a company is given below:

Draw an ogive the given distribution on a graph sheet taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph determine:

1. the median wage
2. the number of employees whose income is below Rs. 8500.
3. if the salary of a senior employee is above Rs. 11500, find the number of senior employees in the company.
4. the upper quartile.

A life insurance agent found the following data for distribution of ages of 100 policy holders.

On a graph sheet draw an ogive using the given data. Take 2 cm = 5 years along one axis and 2 cm = 10 policy holders along the other axis.

Use your graph to find:

1. The median age.
2. Number of policy holders whose age is above 52 years.

Which of the following cannot be determined graphically for a grouped frequency distribution?

A histogram is used to determine:

An ogive is used to determine:

The mean of 7 numbers is 205. If 12 is added to each number, the new mean is ______.

In the formula `barx = a + (sumf_i d_i)/(sumf_i)` for determining the mean of grouped data, d_i's are the deviations from assumed mean ‘a’ of:

The mean of 6 observations 13, 18, 31, 7, 15 and k is 17. The value of k is ______.

The mean of first 10 even natural numbers is ______.

The medians of 33, 44, 37, 56, 57, 40, 36, 34, 53 is ______.

The median of the following observations arranged in ascending order is 64. Find the value of x:

27, 31, 46, 52, x, x + 4, 71, 79, 85, 90