Problem Solving and Data Analysis MCQ Quiz in తెలుగు - Objective Question with Answer for Problem Solving and Data Analysis - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

The mode of a data set is the number that appears most frequently. In option 1, the number 7 appears twice, more than any other number, making it the mode. Option 2 has no repeating numbers, so it has no mode. Option 3 has a mode of 6, and option 4 does not have 7 as the most frequent number. Therefore, the correct data set is 5, 7, 7, 8, 9, making option 1 correct.

Option 4 is correct. The study involved students who were taught using the new method, so the results can be generalized to all such students in the local high school. Option 1 is incorrect because not all students were part of the study. Option 2 is incorrect as it includes students from other schools not involved in the study. Option 3 is incorrect as it generalizes to a broader population beyond the scope of the study.

Given that the ratio $\frac{a}{b}=3$, we can express this as $a=3b$. We also have $\frac{9a}{mb}=3$. Substituting $a=3b$ into this equation gives $\frac{9(3b)}{mb}=3$. Simplifying, we have $\frac{27b}{mb}=3$. Dividing both sides by $b$ results in $\frac{27}{m}=3$. Solving for $m$, we multiply both sides by $m$ to get $27=3m$. Dividing both sides by 3, we find $m=9$. Therefore, the value of $m$ is 9.

The given ratio $\frac{p}{q}=5$ implies that $p=5q$. Substituting this into the second equation $\frac{35p}{tq}=5$ yields $\frac{35(5q)}{tq}=5$. Simplifying, we get $\frac{175q}{tq}=5$. Canceling $q$ gives $\frac{175}{t}=5$. Solving for $t$, we multiply both sides by $t$ to obtain $175=5t$. Dividing both sides by 5 results in $t=35$. Thus, the value of $t$ is 35.

To find out how many widgets the factory produces in a day, we first calculate how many widgets it produces in one hour. At 30 widgets per minute, in one hour (60 minutes), the factory produces 30 × 60 = 1,800 widgets. Since the factory operates for 8 hours a day, the total production in a day is 1,800 × 8 = 14,400 widgets. Therefore, the correct answer is option 1, 14,400 widgets. The other options are incorrect as they do not correctly calculate the widgets produced in a day based on the given rate and operating hours.

The even numbers between 1 and 14 are 2, 4, 6, 8, 10, 12, and 14, making a total of 7 even numbers. Therefore, the probability is $\frac{7}{14}$. Option 1 is the correct choice. Options 2, 3, and 4 incorrectly represent the count of even numbers.

Solution:

We are given:

60% boys → P(Boy) = 0.6

40% girls → P(Girl) = 0.4

8% of boys got 'A' → P(A | Boy) = 0.08

12% of girls got 'A' → P(A | Girl) = 0.12

We are to find: P(Boy | A)

Use Bayes' Theorem:

P(Boy | A) = [P(A | Boy) × P(Boy)] / P(A)

First, compute total probability of getting 'A':

P(A) = P(A | Boy) × P(Boy) + P(A | Girl) × P(Girl)

      = 0.08 × 0.6 + 0.12 × 0.4

      = 0.048 + 0.048 = 0.096

Now, compute P(Boy | A):

P(Boy | A) = (0.08 × 0.6) / 0.096 = 0.048 / 0.096 = 0.5

The problem-solving method is an instructional approach that engages students in identifying, analyzing, and solving problems through critical thinking and inquiry.

Key Points

• Being a structured and inquiry-based approach, the problem-solving method is generally not a time-saving method.
• In fact, it often requires more time than traditional methods because students explore multiple possibilities, gather information, test solutions, and reflect on their findings.
• The focus is on deep understanding rather than quick coverage of content.
• While it is highly beneficial in promoting meaningful learning, it demands considerable classroom time for planning, execution, and discussion.

Hint

•  Helping in the development of scientific attitude is a key strength, as students learn to think logically, question assumptions, and make evidence-based conclusions.
• Training in the scientific method occurs naturally in this approach since learners go through steps such as problem identification, hypothesis formation, experimentation, and evaluation.
• Being a learner-centered method, it places the student at the core of the learning process, encouraging autonomy, curiosity, and active participation.

Hence, the correct answer is time saving method.

Explanation:

Given:

$P(A)=P(\frac{A}{B})=0.25$

and $P(\frac{B}{A})=0.5$

I. $P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}$

⇒ P(A∩B) = P(A) P(B|A)

⇒ P(A∩B) = 0.25 × 0.5 = 0.125

Now

⇒ $P(\frac{B}{A})=\frac{P(A\cap B)}{P(B)}$

⇒ $P(B)=\frac{P(A\cap B)}{P(\frac{A}{B})}$

⇒ $P(B)=\frac{0.125}{0.25}=0.5$

Now, P(A).P(B) = 0.25 × 0.5 = 0.125 = P(A∩B)

Thus  A and B are independent

II. $P(\bar{A}\cup \bar{B})=1–P(A\cap B)$

= 1 – 0.125 = 0.875

III. $P(\bar{A}\cap \bar{B})=1–P(A\cup B)$

= 1 – [P(A) + P(B) – P(A ∩ B)

=  1 – [0.25 + 0.5 – 0.125]

= = 1 – 0.625 = 0.375

So all statements I, II, and III are correct.

∴ Option (d) is correct.

CONCEPT:

Mean and Median of a Data Set

• Mean is the average of all data values:

  Mean = (Sum of all values) / (Number of values)

• Median is the middle value when the data is arranged in ascending order.
• For an even number of values, median = average of the two middle terms.

EXPLANATION:

• Given data: {25, 29, 25, 32, 24, x}
• Mean = 27
• Total sum = 6 × 27 = 162
• Sum of known values = 25 + 29 + 25 + 32 + 24 = 135
• So, x = 162 − 135 = 27

Final data set: {24, 25, 25, 27, 29, 32}

• Arrange in ascending order: 24, 25, 25, 27, 29, 32
• Middle two values = 25 and 27
• Median = (25 + 27) / 2 = 26

Correct answer  26