Problem Solving and Data Analysis MCQ Quiz in मल्याळम - Objective Question with Answer for Problem Solving and Data Analysis - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

To maintain a median of 75, the 8th and 9th numbers in the ordered data set must average to 75. The numbers provided are 65, 66, 68, 70, 72, 73, 74, 76, 77, 78, 80, 82, 84, 86, and 88. Adding 74 as the 16th number maintains the median, as the median will be the average of the 8th and 9th numbers (74 and 76), resulting in $\frac{74+76}{2}=75$.

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

m = x₂−x₁/ y_2​ − y_1​​

Substituting the points (x1,y1)=(2,18)Unknown node type: span" id="MathJax-Element-8-Frame" role="presentation" style="position: relative;" tabindex="0">(x1,y1)=(2,18)Unknown node type: span$(x_1,y_1)=(2,18)\; <merror><mtext>Unknown\; node\; type:\; span</mtext></merror>$ (x1,y1)=(2,18)<span style="font-family: var(--bs-body-font-family); font-size: var(--bs-body-font-size); font-weight: var(--bs-body-font-weight); text-align: var(--bs-body-text-align);"> </span> (x2,y2)=(5,22) (x_2, y_2) = (5, 22)" id="MathJax-Element-9-Frame" role="presentation" style="position: relative;" tabindex="0">(x2,y2)=(5,22)$(x_2, y_2) = (5, 22)$ $(x_2, y_2) = (5, 22)$

 

$$m = \frac{22 - 18}{5 - 2}$$ m=43=1.33

 

The slope m m" id="MathJax-Element-13-Frame" role="presentation" style="position: relative;" tabindex="0">m$m$ $m$  of the best-fit line is 1.33, meaning for every 1 unit increase in X, Y increases by 1.33 units. $$m = \frac{4}{3} = 1.33$$