For some data x_1, x_2, …, x_n with respective frequencies f_1, f_2, …, f_n, the value of i=1^n f_i (x_i-x ) is equal to: (A) nx (B) 1 (C) f_i (D) 0

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 9

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQStatistics

For some data $x_{1}, x_{2}, \dots, x_{n}$ with respective frequencies $f_{1}, f_{2}, \dots, f_{n}$ , the value of $\sum_{i = 1}^{n} f_{i} (x_{i} - \overset{x}{ˉ})$ is equal to:

(A) $n \overset{x}{ˉ}$
(B)1
(C) $\sum f_{i}$
(D)0

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Expand the bracket inside the sum.

Hint 2

Use the definition $\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$\sum f_{i} (x_{i} - \overset{x}{ˉ}) = \sum f_{i} x_{i} - \overset{x}{ˉ} \sum f_{i}$ .
Since $\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}$ , we have $\overset{x}{ˉ} \sum f_{i} = \sum f_{i} x_{i}$ , so the expression equals $0$ . The answer is option (D).
1 mark

Answer: 0, option (D)

Where the marks are

Uses $\sum f_{i} x_{i} = \overset{x}{ˉ} \sum f_{i}$ to get 0, option (D) (1 mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 9

Hints

Step-by-step solution

Revise the chapter

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