Statistics Questions

Statistics is a field of mathematics or a corpus of mathematics concerned with data gathering, analysis, interpretation, and presentation. Statistics is sometimes seen as a distinct mathematical discipline rather than a mathematical subject. While data is employed in many scientific efforts, statistics is concerned with how to interpret data in the face of ambiguity and how to make decisions when faced with doubt.

Statistics:

Statistics is a term that describes the study and manipulation of data. As we mentioned in the beginning, statistics is concerned with the analysis and processing of numerical data. Let’s have a look at some more statistics definitions from different authors.

Statistics Questions:

Q1. Give two examples of data collection in everyday Life.

Solution. A. Our country’s population has risen in the last two decades.

B. In a classroom, the number of tables and chairs.

Q2. If the following marks were received by pupils in a class test:

55 36 95 73 60 42 25 78 75 62 35 36 95 73 60 42 35 36 95 73 60 42 35 36 95 73 60 

Then, in order of lowest to highest, organize the marks.

Solution: We must organize each student’s grades in ascending order as follows:

25 36 42 55 60 62 73 75 78 95 73 75 78 95 73 75 78 95 73 75 78 95 73 

Q3. Check out the frequency distribution table below, which contains the weights of 38 students in a class:

 (i) For classes 31–35, what is the class-interval?

(ii) How many kids weigh between 41 and 45 kilograms?

Solution. (i) Upper class limit – lower class limit = 35-31= 4 class interval

(ii) There are 14 students in the 41-45 age group.

Q4. Consider a tiny production unit with only five workers: a supervisor and four laborers. The employees are paid Rs. 5,000 per month, while the supervisor is paid Rs. 15,000 per month. Calculate the wages’ mean, median, and mode.

Solution. Mean = (5000 + 5000 + 5000 + 5000 + 15000)/5 = 35000/5 = 7000

So, the mean salary is Rs. 7000 per month

Let’s arrange the wages in increasing order to get the median:

5000, 5000, 5000, 5000, 15000

Median = (n+1)/2 = (5+1)/2 = 6/2 = 3rd observation

Median = Rs. 5000/-

The number of times an observation is repeated is referred to as the mode = Rs.5000/-

Q5.  A survey was undertaken to determine the heights (in cm) of 51 females in Class X of a school, and the following information was obtained:

Find the median height:

Solution. Take a look at the following table:

n = 51

n/2 = 51/2 = 25.5

This observation was made in class145 – 150.

L (the lower limit) = 145,

Cf (the previous class’s cumulative frequency 145 – 150) = 11

F (the frequency of the 145–150 median class)= 18,

H (the class size) = 5

Using the formula,

Q6. The number of wickets taken by bowlers in one-day cricket matches is shown in the table below. Using the right procedure, calculate the average number of wickets. What does the term “mean” mean?

Solution. The class sizes vary, and the class marks (xi) are significant. Use the step deviation method for a = 200 and h = 20.

SO, ʉ = -106/45

X̄ = 200+20(-106/45) = 200 – 47.11 = 152.89

As a result, these 45 bowlers have taken 152.89 wickets in one-day cricket on average.

Conclusion:

The degree to which conclusions about the relationship between variables based on data are correct or “logical” is referred to as statistical conclusion validity. This started out as a debate over whether the statistical conclusion regarding the link between the variables was valid, but today there is a push for “reasonable” conclusions based on quantitative, statistical, and qualitative data. There are two types of errors that can occur: type I (looking for a difference or correlation when none exists) and type II (looking for a difference or correlation when none exists) (finding no difference or correlation when one exists).The aspects of the study that make these types of errors more likely are referred to as statistical conclusion validity. The employment of proper sample processes, appropriate statistical tests, and trustworthy measuring procedures are all part of statistical conclusions validity.