## Introduction

The process in mathematics that synthesizes raw numerical information into more insightful and understandable figures is called *Statistics*.

You can access *LeadingLearners* and their CBSE class 10 maths study material to learn statistics better. In the class 10 maths chapter: ‘Statistics’, you will learn about the collection, presentation, graphical plotting of data, and various methods to quantify a numerical dataset based on its values.

## Maths Chapter - Statistics (Chapter-level Description)

Statistics is the study and synthesis of raw, numerical information into meaningful figures that can be understood easily. In this chapter, you will learn how to deal with data in four important steps.

Let's see what they are. On the website, you can find study material and doubt solvers for better understanding.

## Data Collection

The first important step in processing any kind of information is *data collection*. Based on how a set of data was collected, it can be classified into two categories:

### Primary Data

When you are collecting data yourself, first-hand, it is called *primary data*. This data is verified and reliable since you collected it yourself.

### Secondary Data

When you seek data from another person, this becomes secondary data because it is second-hand. You should always be careful when asking for secondary data because you will need to verify its source.

## Data Presentation

In order to make sense of the raw data collected in the first step, it is important to present it in a way that is easy to understand. There are certain ways this is done in *Statistics*.

### Ascending/Descending Order

You can arrange the number of pens with each student in your class in ascending/descending order to help you better understand the data.

### Frequency of Data

When the dataset is large, you can count the number of times the same value occurs in the set. This is the *frequency* of that number.

### Classes of Data

In a table containing frequency information of your data, you can further compress the data by creating classes. For example, Roll no. 1 to 9 is Group One, 10 to 19 is Group Two, and so on. These are called classes. The number of items in one class is called *class-size or class-width*. The highest and lowest values in each class are called *upper* and *lower* class limits. Additional information is available in CBSE class 10 maths video lessons on the website.

## Graphical Representation

There are three ways data can be represented graphically:

### Bar Graphs

A bar graph represents data with two distinct attributes plotted on the (x) and (y) axes of a graph.

### Histograms

A histogram is a bar graph that represents continuous classes. Whereas a bar graph has a horizontal space between each bar, a histogram does not.

### Frequency Polygons

A frequency polygon is a line drawn through the mid-points of the top of each bar on a histogram.

## Central Tendency

Another meaningful way to deal with data is to find a central value that can be representative of the entire dataset. There are three ways this can be done:

### Mean

The *mean* of a dataset is the sum of all values divided by the total number of values.

### Median

The median of a dataset is the middle value of the dataset when arranged in order.

### Mode

The value that has the highest frequency in a dataset is called the *mode*. You can understand this better through the maths NCERT solutions chapter solution.

## Exercises

Through these NCERT solutions for CBSE class 10 maths, you will learn to calculate central tendencies of the data presented, find missing frequencies and plot the data on graphs. You can also access the study material on this website for a more thorough understanding of CBSE class 10 mathematics.

### Exercise 14.1

#### Solution 1

In this solution, you can solve for the mean by calculating the class mark first. Then by using the direct mean method, you can calculate the mean. You can access the resources for the most important questions on the website.

#### Solution 2

This solution arrives at the mean daily wages of the factory workers by using the *step-deviation method*, which involves finding out the class mark and total frequency.

#### Solution 3

In this solution, you can calculate the missing frequency using the *assumed mean method* by solving the formula equation for the missing number.

#### Solution 4

The average beats per minute for women in this solution can be calculated simply by using the *step-deviation method*. You will need to calculate the deviation value first.

#### Solution 5

This solution employs the *step-deviation method* to calculate the mean. However, since there is a gap of 1 between class values, the exercise of adding 1/2 to the upper-class limit and subtracting 1/2 from the lower class limit is performed first.

#### Solution 6

In this solution, you use the step-deviation method to solve for the mean daily expenditure on food.

#### Solution 7

The concentration of SO2 in the air can be found out by solving for the deviation from the assumed mean and then applying the step-deviation formula for calculating the mean ppm value.

#### Solution 8

This solution employs the assumed mean method to solve for the mean number of days the student was absent. It begins by calculating the class mark and solving for deviation for each class.

#### Solution 9

By using the step-deviation method, you can solve for the mean literacy rate. To start, the solution begins by calculating the values required for the formula of the step-deviation method.

### Exercise 14.2

#### Solution 1

This solution aims to calculate the mean and the mode of the ages of the patients admitted to a hospital. It uses the standard-deviation method to calculate the mean. For the mode, you can use the modal class method for calculations.

#### Solution 2

The solution involves calculating the modal lifetime of electrical components from the given data. Proceed by locating the values needed for the modal class formula, and calculating the mode thus.

#### Solution 3

This solution aims to find the mean monthly expenditure and modal monthly expenditure. It is a straightforward solution involving the use of the modal class method and the standard-deviation method to arrive at the answer.

#### Solution 4

The solution goes to find out the mean teacher-student ratio in various states and UTs using the standard-deviation method. It also calculates the modal value of this ratio, comparing all the states and UTs using the modal class formula.

#### Solution 5

In this solution, a straightforward calculation for the mode using the modal class formula is used. List down the values required for the formula, and calculate.

#### Solution 6

The mode for the cars is calculated using the modal class formula, after listing down the values for modal frequency, preceding and succeeding frequencies, class size, and lower limit of the modal class.

### Exercise 14.3

#### Solution 1

This solution calculates the mean, mode, and median of a dataset of consumers. Use the standard-deviation formula to calculate the mean. Using the modal class method, the mode can be calculated easily. Now, since it is a grouped set of data, the median cannot be calculated simply by counting. Therefore, use the median formula for grouped datasets.

#### Solution 2

This solution aims to calculate the missing frequencies by using the formula for median and then solving for the unknown variables. Since it is a grouped dataset, the median cannot be calculated by simply finding the middle value. Use the formula.

#### Solution 3

In this solution, the dataset is presented in a grouped manner. Therefore, to calculate the median, the formula is applied. From the given cumulative frequency, find out the median class using N/2, then solve the formula for the median.

#### Solution 4

In this solution, you are presented with grouped data with a gap in intervals. Therefore, add and subtract 1/2 from the upper and lower class limits to get a continuous dataset. Then proceed to find the median class and use the median formula for the answer.

#### Solution 5

The solution beings by first calculating the cumulative frequencies for the data presented. Then, using N/2, the median class is pinpointed. To find the median, the formula is applied since this is grouped data.

#### Solution 6

In this solution, proceed by calculating cumulative frequencies, followed by solving for the median using its formula. Then, calculate the class-mark and find the mean using the standard deviation method. Lastly, the mode can be calculated using the relationship equation between the mean, median, and mode.

#### Solution 7

This solution shows straightforward calculations for the median by calculating the cumulative frequencies first, then solving for the median class. The median formula is then used to arrive at the answer.

### Exercise 14.4

#### Solution 1

This solution aims to plot a histogram using the data provided. First, calculate the cumulative frequencies of all the classes. Next, plot the classes on the (x) axis, and the cumulative frequencies on the (y) axis.

#### Solution 2

This solution aims to verify the median value obtained from a histogram with the value obtained from the median formula. Using the cumulative frequencies provided, plot a histogram with classes on the (x) axis. Proceed to use the formula of the median to verify.

#### Solution 3

This solution plots an ogive using the cumulative frequencies and class intervals provided in a table. Use these NCERT statistics solutions to learn Statistics better.