Statistics Class 10 Study Notes

Statistics is an essential tool to conduct and present the correct analysis of a given data and observation. The foundation of learning this mathematical concept begins in class 10. Mathematics is one of those subjects that cannot be learned by just reading the concepts and explanations, it needs strong and regular practice to achieve exceptional outcomes and master it. In this blog, we will be covering Statistics class 10 study notes!

What is Statistics?

The word “Statistics” is a branch of mathematics that involves the collection, classification, analysis, and representation of data. It assists in attaining important insights from the data, and thus, in making beneficial decisions based on the data. So, let us dive deeper into these Statistics class 10 study notes.

Also Read: Surface Area And Volume Class 10 Maths

Mean of Grouped Data

As you might have studied in your previous classes, the Mean of a particular data set is the summation of all the quantities divided by the number of quantities. If you recollect that if x1, x2,…, xn are observations with frequencies f1, f2,…, fn respectively, then this means that observation x1 happens f1 times, x2 happens f2 times, and so on. The formula of mean is given by,

            Mean = (f1 * x1 + f2 * x2 + … + fn * xn) / ( f1 + f2 + … + fn)

This formula is useful and good for generally ungrouped data and when the data set is not very big. But, in our worldly lives, the data is so extensive that for doing precise research, it is required to be consolidated into a group. Let us see how we can do this with an example. Take a look at the question given below:

The data presented to us above is grouped by allocating class-intervals of size 2 (the difference between each observation). While allotting frequencies, have in mind that in every class-interval the number of plants befalling in any upper class-limit would be counted in the next class. With that in remembrance, we will create a table of our own.

If you look at the image above, we have defined the frequencies (fi) which were presented to us. For finding the value of xi, we need a point that would serve as the representative of the whole class. It is supposed that the frequency of every class-interval is clustered around its central point. So, the central point (or in our case the number of plants) of every class can be taken to describe the observations befalling in the class. We get the central point of a class by determining the average of its uppermost and lowermost limits. Given by,

xi = (Uppermost class limit + Lowermost class limit) / 2

We can now calculate the Mean in the same way by using the formula for Mean as discussed earlier

Mean = (Sum of fi * xi) / (Sum of fi) = 162 / 20 = 8.1

The above-denoted method is called the direct method and is beneficial when the given numerical value is small.

But, when the numerical values of xi and fi are big, obtaining the product of xi and fi grows tiresome and long. So, for the before-mentioned circumstances, there is a different process termed as the assumed mean method. In this method, we break each xi to a tinier number so that our estimations become simple. The assumed mean method is calculated by the formula:

where,  A or a = assumed mean
fi = frequency of ith class
di = xi – a = deviation of ith class
xi = class mark = (upper limit + lower limit) / 2
Σfi = total number of observations

We can also calculate mean by a third method known as the step-deviation method, and can be calculated by the formula below:

where, A or a = assumed mean
h = class size of each class interval
ui = (xi – a) / h
fi = frequency of ith class
Σfi = total number of observations

Mode of Grouped Data

As you know, Mode is the value that occurs the most number of times. But mostly we have calculated Mode for ungrouped data. We will now see how we can obtain the Mode of a grouped data set. Let us consider the following example to demonstrate this method. These Statistics class 10 study notes help you in learning further about this. Suppose we have been given the data below and we have to find the Mode of the following frequency distribution:

As you can see, we can’t determine the Mode by just looking at the data. We can simply find a class with the maximum frequency, known as the modal class. The Mode is a value present in the class with the highest frequency and is given by the formula:

l = lower limit of the class with the highest frequency
h = size of the class interval (assuming all class sizes to be equal)
f1 = frequency of the class with the highest frequency
f0 = frequency of the class preceding the class with the highest frequency
f2 = frequency of the class succeeding the class with the highest frequency

In our above example, the maximum frequency is 12, and it belongs to class 10 – 20
So, the modal class will be 10 – 20

Therefore, modal class = 10 – 20, lower limit (l) = 10 and class size (h) = 10 (20 – 10)

Frequency of the modal class or f1 = 12,  frequency of the class preceding the modal class f0 = 8, and frequency of the class succeeding the modal class or f2 = 10

Since we now have all the variables let us substitute all of them in our formula,

Thus, Mode = 16.67

Median of Grouped Data

The next topic in Statistics class 10 is Median. The Median is defined as the middle value of the data set, or it is a measure of central tendency which gives the value of the middle-most observation in the data, and the data set should be arranged in either decreasing or increasing order. For finding Median if n or number of observations is odd, the formula is ((n + 1) / 2)th observation, while for even number of observations it is (n / 2)th observation. But, this doesn’t work for grouped data sets, so we find the class which contains the Median. To find out the Median, we first calculate the cumulative frequency and then compare whose cumulative frequency is nearest to and greater than n / 2, where n denotes the number of observations. This is known as the median class, and once we have our median class, we can then apply the formula below for determining the Median,

To better understand this concept, let us go through an example of Statistics class 10. An insurance representative has been provided with the table (refer to the image below) for ages till 100 of policyholders. We have to find the median age if policies are sold only to persons whose age is above 18 years and less than 60 years.

So, the first step is to form a separate column and calculate the cumulative frequency distribution for the above data as,

Then we calculate,

By comparing the cumulative frequency from the table with n / 2, we see that the median class nearest to or greater than 50 is 78. Now we have h = 5, f = 33, cf = 45, l = 35, and n / 2 = 50; we now substitute these values in our formula and we get,

By solving, we get Median = 35.76 years.

Representing Cumulative Frequency Distribution on Graphs – Statistics Class 10

Since we have done a lot of calculations, it is a good time to see and visualize how these data sets look, as it will help us in understanding the given data by looking at it and make it easier. In this section, we will describe a cumulative frequency distribution with the help of graphs. For describing the data using graphs, we consider the uppermost limits of the class intervals on the horizontal axis (x-axis) and their analogous cumulative frequencies on the vertical axis (y-axis), picking a suitable scale. The scale may not be the same on both the axis. By plotting all the points and joining them by a free hand, the curve obtained is called a cumulative frequency curve, or an ogive.

So, to summarize, we got to learn about statistics class 10 chapter 14. We believe we assisted you in understanding the world of Statistics and clarified some concepts. Statistics is an extensive chapter and having a grip on the topic gives you an advantage in the examinations. If you want to learn more or want to gain insight into different subjects, Leverage Edu has a variety of study notes that can help you so do.