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There is a gap of 1 between two class intervals. Therefore, has to be added to the upper class limit and has to be subtracted from the lower class limit of each interval. Taking 57 as assumed mean a , d i , u i , f i u i are calculated as follows. Step deviation method is used here as the values of f i, d i are big and also, there is a common multiple between all d i.

Taking as assumed mean a , d i , u i , f i u i are calculated as follows. To find out the concentration of SO 2 in the air in parts per million, i. Taking 0. A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. Taking 17 as assumed mean a , d i and f i d i are calculated as follows.

The following table gives the literacy rate in percentage of 35 cities. Find the mean literacy rate. Taking 70 as assumed mean a , d i , u i , and f i u i are calculated as follows. Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency. Taking 30 as assumed mean a , d i and f i d i are calculated as follows.

Mean of this data is It represents that on an average, the age of a patient admitted to hospital was Mode is It represents that the age of maximum number of patients admitted in hospital was The following data gives the information on the observed lifetimes in hours of electrical components:.

The following data gives the distribution of total monthly household expenditure of families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure. Taking as assumed mean a , d i , u i , and f i u i are calculated as follows.

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures. The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

A student noted the number of cars passing through a spot on a road for periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them. Taking as assumed mean a , d i , u i , f i u i are calculated according to step deviation method as follows.

If the median of the distribution is given below is A life insurance agent found the following data for distribution of ages of policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year. Here, class width is not the same. There is no requirement of adjusting the frequencies according to class intervals. The given frequency table is of less than type represented with upper class limits.

The policies were given only to persons with age 18 years onwards but less than 60 years. Therefore, class intervals with their respective cumulative frequency can be defined as below. Number of policy holders f i. The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:.

Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to The given data does not have continuous class intervals. It can be observed that the difference between two class intervals is 1. Therefore, has to be added and subtracted to upper class limits and lower class limits respectively. From the table, it can be observed that the cumulative frequency just greater than is 29, belonging to class interval Determine the median number of letters in the surnames.

Find the mean number of letters in the surnames? Also, find the modal size of the surnames. Therefore, median number and mean number of letters in surnames is 8. The distribution below gives the weights of 30 students of a class.

Find the median weight of the students. Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Taking upper class limits of class intervals on x -axis and their respective frequencies on y -axis, its ogive can be drawn as follows. During the medical check-up of 35 students of a class, their weights were recorded as follows:.

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula. Taking upper class limits on x -axis and their respective cumulative frequencies on y -axis, its ogive can be drawn as follows.

Mark the point A whose ordinate is Therefore, median of this data is It can be observed that the difference between two consecutive upper class limits is 2.

The class marks with their respective frequencies are obtained as below. Taking the lower class limits on x -axis and their respective cumulative frequencies on y -axis, its ogive can be obtained as follows. Bar graphs , histograms , and frequency polygons were also explained earlier.

In this chapter, the study of three measures namely mean , median and mode from ungrouped data to that of grouped data will be extended. Concept of cumulative frequency , the frequency distribution cumulative and drawing of cumulative frequency curves Ogive is discussed in this chapter. Firstly, the topic of Mean of Grouped Data is explained. The first solved example is based on the concept of finding the mean of the given data here marks.

These types of questions must be solved in tabular form. After that, the upper limit and the lower limit are explained. It is assumed that the frequency of each class is centered around its midpoint. The direct method is explained with the help of a solved example. Another method known as the assumed mean method is also explained. After that, Step deviation method to calculate the mean of the given data is explained. Exercise The next section deals with the concept of Mode of grouped data.

The class with the maximum frequency is called the modal class. Mode can be equal , less or more than mean. After that students will learn about the Median of Grouped Data. Median can be calculated using the formula and by using the ogive curve. There is also an important relation between mean, median and mode that can be studied in this chapter. Chapter 1 - Real Numbers. Chapter 2 - Polynomials.

Chapter 4 - Quadratic Equations. Chapter 5 - Arithmetic Progressions. Chapter 6 - Triangles. Chapter 7 - Coordinate Geometry. Chapter 8 - Introduction to Trigonometry. Chapter 9 - Some Applications of Trigonometry. Chapter 10 - Circles. Chapter 11 - Constructions.

Chapter 12 - Areas Related to Circles. Chapter 13 - Surface Areas and Volumes.

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