Introduction of Statistics and its Types
Statistics are studied in CBSE across standards IX, X and XI. Even basic statistics questions demand a certain degree of conceptual clarity and thorough practice. Practicing more and more problems will equip students with the necessary skill to ace the examination and score significantly higher.
Before proceeding to solve a few statistics important questions, it is important to recapitulate the concept inherent to this branch of Mathematics. Statistics comprises such mathematical analysis which undertakes quantification, representation and concluding a given set of data.
What is Statistics?
Statistics is the branch of science that studies and develops methods for gathering, analyzing, interpreting, and presenting empirical data. Statistics is a very interdisciplinary field; statistics study has applications in almost all scientific fields, and research concerns in diverse scientific fields drive the development of novel statistical methods and theories. Statisticians use a variety of mathematical and computational techniques to develop approaches and analyze the theory that underpins them.
Uncertainty and variation are two key concepts in statistics. There are numerous circumstances in science (and, more broadly, in life) where the conclusion is unknown. In some circumstances, the uncertainty stems from the fact that the outcome has not yet been determined (for example, we may not know whether it will rain tomorrow), while in others, the doubt stems from the fact that the conclusion has already been established but we are unaware of it (e.g., we may not know whether we passed a particular exam).
Terminologies used in Statistics
Population - It is actually a group of people, objects, or events whose properties are to be investigated.
Sample - It's a subset of a larger population.
Types of Statistics
Statistics are mainly categorized into two types:
1. Descriptive Statistics
2. Inferential Statistics
Descriptive Statistics: Descriptive statistics makes use of data to describe a population through numerical calculations, graphs, and tables. It presents data in a graphical format. It is simply used to summarise objects, among other things.
Data is typically arranged and displayed in tables or graphs summarizing details such as histograms, pie charts, bars or scatter plots.
Descriptive Statistics are just descriptive and thus do not require normalization beyond the Data collected.
Inferential Statistics- Inferential Statistics uses a sample of data from the population to form inferences and predictions about the population. It uses probability to derive a conclusion after generalizing a huge dataset. Its sole purpose is to clarify the meaning of descriptive statistics. Its sole purpose is to study, interpret, and draw conclusions. Inferential statistics is primarily concerned with and linked to hypothesis testing, the goal of which is to reject the null hypothesis.
Mean, Median and Mode in Statistics
a) Mean - It is a metric for calculating the average of all values in a sample set.
b) Median - It is a measure of a sample set's central value. The data set is sorted from the lowest to the highest value, and then the precise middle is determined.
c) Mode - It is the most common value in the sample set. The value that appears most frequently in the core set is really mode.
Variability Measurement in Statistics
The measure of Variability often called a measure of dispersion, is a term used to describe the variability in a sample or population. There are three common measures of variability in statistics, as indicated below:
Range- It is a measurement of how values in a sample set or data set are spaced apart.
Range= maximum value-minimum value
Variance- It simply expresses how far a random variable deviates from its expected value and can be calculated as square of deviation.
\[S^2 = \sum_{i=1} ^{n} (x_i - \bar {x})^2 \div n\]
n represents total data points, x represents mean of data points, and xi represents individual data points in these formulas.
Dispersion- It is a measure of how far a set of data deviates from its mean.
σ = \[\sqrt{(1 \div n) \sum _{i=1} ^{n} (x_i - \mu)^2}\]
Simple Statistics Questions
Here are some of the basic statistics questions and answers to solve and practice.
Question 1: For Which Value of ‘a’, Mode of the Following Data is 3:
4, 5, 6, 3, 5, 4, 3, 5, 6, 3, 3
(a) 5
(b) 6
(c) 3
(d) 4
Solution: The answer is option (c) 3.
Mode amounts to be the most common value within a given data set. Within the set, 3 appears four times which makes it mode in the series.
Question 2: Value of Mean and Mode are Given as 30 and 15, respectively. Value of Median is -
(a) 25
(b) 26
(c) 24.5
(d) 22.5
Solution: The answer is option (a) 25. The relation between mean, median and mode is, Mean – Mode = 3 (Mean – Median). Substituting the value, the equation becomes 30 – 15 = 3 (30 – Median). On solving, the median comes to 25.
Question 3: Which of the Following Holds for Mode?
(a) It is the most frequent value
(b) It is somewhere in the middle in terms of frequency
(c) It is the least frequent value
(d) None of the above is correct
Solution: The answer is option (a). The definition of mode indicates that it is the repeatedly occurring value within a given data series.
Question 4: Which Among the Following Cannot be Represented Graphically?
(a) Median
(b) Mean
(c) Mode
(d) None of the above option
Solution: The answer is an option (b). Mean is a specific value derived from the sum of all values and divided by the number of times of values. Given that this value is single and cannot be made to undergo a comparison with other values, its graphical representation is not feasible.
Question 5: In Case of Computation of Mean within a Grouped Data, the Assumption is that Frequencies are -
(a) Centered at lower limit among classes
(b) Centered at upper limit among classes
(c) Evenly placed across all classes
(d) Centered within class marks among classes
Solution: An answer is an option (d). In the computation of the mean of grouped data, the frequencies are always located at the center within the class marks.
Question 6: Which of the Following is Determined by Constructing a Cumulative Frequency Table?
(a) Median
(b) Mean
(c) Mode
(d) None of the above option
Solution: An answer is an option (a). The median of a series is determined with the help of the cumulative frequency table.
Uses of Statistics in Real-life
In every subject of study, statistics aids in the effective and efficient design of a statistical enquiry.
Statistics aids in the collection of useful quantitative data.
Statistics aids in the presentation of complex data in a tabular, diagrammatic, or graphic format for easy and clear comprehension.
Through quantitative measurements, statistics aids in understanding the nature and pattern of variability of a phenomenon.
Statistics aids in the drawing of correct inferences about population parameters from sample data, as well as a measure of their reliability.
It keeps us up to date on what is going on in the world around us. Statistics are crucial because we live in an information age, and most of that information is based on mathematical calculations. It indicates that accurate data and statistics principles are required.
Practising basic Statistics questions is imperative to score high in examinations. Moreover, all the queries that you may have related to this topic should be clarified at the earliest. To that effect, you can avail Vedantu’s online classes and have all your queries answered. Download the app today!
FAQs on Statistics Questions
1. What is the Statistics Syllabus in CBSE Class 10?
The syllabus of Statistics in CBSE class 10 includes – (1) Introduction to Statistics, (2) Mean (Grouped Data), (3) Mode (Grouped Data), (4) Median (Grouped Data), and (5) Graphical representation of cumulative frequency distribution.
For preparing questions on Statistics with answers, it is essential to be familiar with the syllabus at the beginning. It would ensure that no topic is missed in the course of preparation.
2. What is the Method to Prepare Statistics Basic Questions for CBSE Class?
Before starting with the preparation of statistics theory questions and answers, a student should first determine the method of study. It is better to start with possible questions as that would allow understanding important topics requiring more attention and focus.
Also, take note of the various marks of questions in basic statistics question. For instance, questions can be of 3 marks, 2 marks or even 1 mark. The answers to these questions have to be prepared following the marks allotted to each question.
3. What are the Different Models Covered in Common Statistics Questions?
Various models which may be included in statistics theory questions are – (1) mean, (2) regression analysis, (3) skewness, (4) kurtosis, and (5) variance, among others.
Students should also be aware that there are different methods of description of data. Some of those methods include mean, median, mode, range etc.
4. Find the median from the following table:
Cars | Mileage | Cylinder |
Swift | 21.3 | 3 |
Verna | 20.8 | 2 |
Santro | 19 | 5 |
i20 | 15 | 4 |
Solution: For finding out the median, let us arrange the above data in an ascending order:
15
19
20.8
21.3
Median for even number of data = \[\frac {(b+c)}{2}\]
= \[\frac {(19+20.8)}{2}\]
Therefore, we get a median of 19.9.
5. List the types of inferential statistics.
One sample test of difference/One sample hypothesis test
Confidence Interval
Contingency Tables and Chi-Square Statistic
T-test or Anova
Pearson Correlation
Bi-variate Regression
Multivariate Regression
6. Describe the importance of user mode.
The mode is simple to grasp and compute.
Extreme values have no effect on the mode.
In a data collection and a discrete frequency distribution, the mode is easy to spot.
For qualitative data, the method is useful.
An open-ended frequency table can be used to calculate the mode.
7. List a few disadvantages of statistics.
Ignored Qualitative Aspect
Individual objects are not dealt with
It doesn't tell the whole tale of phenomenon
It's easy to get it wrong
Laws aren't always exact
The following results are only true on average
There are too many approaches to studying problems.