JKSSB Statistics MCQs

Explanation

The new correlation coefficient will be B) -0.5.

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Fisher's Ideal Index Number does not satisfy the C) Circular Test.

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The total fertility rate per woman is B) 2.7.

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The net reproductive rate is D) 4.

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The percentage of male employees in the company is A) 40%.

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The approximate value of $f(10)$ using Lagrange's interpolation formula is B) 14.67.

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The correct answer is B) Life expectancy.

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The correct answer is A) Crude death rate.

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Zero should be used only to indicate the C) Quantity of variable.

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Primary data is original data collected by the researcher specifically for the purpose of the study.

Explanation

To find the probability, we need two numbers:

The total number of ways to scramble the word.

The number of ways to scramble the word where the vowels are grouped together.

Step 1: The Total Possible Arrangements

The word STATISTICS has 10 letters in total.

Because some letters repeat, we have to divide the total number of combinations by the combinations of those repeating letters so we don't double-count them.

Total letters: 10 (which gives us 10!)

Repeating S: 3 (so we divide by 3!)

Repeating T: 3 (so we divide by 3!)

Repeating I: 2 (so we divide by 2!)

The Math:

Total Ways = 10! / (3! x 3! x 2!)

Total Ways = 3,628,800 / (6 x 6 x 2)

Total Ways = 3,628,800 / 72

Total Ways = 50,400

Step 2: The "Vowels Together" Arrangements (The Box Method)

We want the vowels to always stay together. The easiest way to visualize this is to pack all the vowels into a single, movable box.

The vowels are A, I, I. We put them in our box: [A, I, I]

The leftover consonants are: S, S, S, T, T, T, C

Part A: Arranging the Box and the Consonants

Instead of arranging 10 individual letters, we are now arranging 8 units: the 1 box + the 7 consonants.

Just like in Step 1, we find the combinations for these 8 units and divide by the repeating consonants (the three S's and three T's).

Ways to arrange the 8 units = 8! / (3! x 3!)

Ways to arrange the 8 units = 40,320 / (6 x 6)

Ways to arrange the 8 units = 40,320 / 36 = 1,120

Part B: Arranging the Letters Inside the Box

The vowels are stuck together in the box, but they can still shuffle around with each other (for example, A-I-I or I-A-I).

There are 3 letters in the box, and the letter "I" repeats twice.

Ways to arrange inside the box = 3! / 2!

Ways to arrange inside the box = 6 / 2 = 3

Part C: The Total Favorable Ways

For every single one of the 1,120 ways you can arrange the outer units, there are 3 ways to shuffle the vowels inside the box. So, we multiply them.

Total ways vowels are together = 1,120 x 3

Total ways vowels are together = 3,360

Step 3: The Final Probability

Probability is the number of ways we get what we want (vowels together) divided by the total number of things that could happen (total arrangements).

Probability = 3,360 / 50,400

Probability = 1/15

Explanation

The correct answer is B) 3.

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The correlation between $y$ and $x$ is A) Positive.

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The minimum percentage of students who must have passed both subjects is B) 55%.

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The correct statement is A) Data are inconsistent.

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the value of $x$ is 1.12.

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The predicted life expectancy in the year 2025 would be D) 81 years.

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The probability that at least two events occur is $\mathbf{19/60}

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The median is equal to C) 68.

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The correct answer is B) 95.04.

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The correct statement is:

Less reliable

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Girls Kho-Kho=13, Boys Cricket=23, Boys Volleyball=13, Total boys=60. Correct matching is option A.

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Mean=6.125, Median=7, Mode=7, Sample size=8. Order: d(8) > b(7) > a(6.125) > c(7). So correct is d, b, a, c.

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Tabulation allows comparison both row-wise and column-wise. Hence (d) is false.

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Statements (b) and (d) are correct. A pilot test is recommended, so (c) is wrong.

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Primary data is collected first-hand through interviews, surveys, observations, etc.

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Secondary data refers to data already collected, e.g., from databases, published reports.

Explanation

Fabricating data to arrive at the desired conclusion