What is the mean mark?

Question

ScanSolve AI Tutor · Accepted Answer

Here is the frequency distribution table:

Marks ( $x$ )	No. of students ( $f$ )
1	11
2	12
3	10
4	17
5	16
6	15
7	14
8	13
9	12

18. What is the mean mark?

To find the mean mark, we use the formula:

\text{Mean} = \frac{\sum (f \times x)}{\sum f}

Calculate the sum of (frequency $\times$ mark), $\sum (f \times x)$ .
$\sum (f \times x) = (1 \times 11) + (2 \times 12) + (3 \times 10) + (4 \times 17) + (5 \times 16) + (6 \times 15) + (7 \times 14) + (8 \times 13) + (9 \times 12)$ $\sum (f \times x) = 11 + 24 + 30 + 68 + 80 + 90 + 98 + 104 + 108$ $\sum (f \times x) = 613$
Calculate the total number of students, $\sum f$ .
$\sum f = 11 + 12 + 10 + 17 + 16 + 15 + 14 + 13 + 12$ $\sum f = 120$
Calculate the mean mark.
$\text{Mean} = \frac{613}{120}$ $\text{Mean} \approx 5.1083$
Rounding to the nearest whole number, the mean mark is 5.

The correct option is C.
$\boxed{\text{C. 5}}$
19. What is the modal mark?

The modal mark is the mark with the highest frequency (number of students).
Identify the highest frequency from the "No. of students" row.
The frequencies are 11, 12, 10, 17, 16, 15, 14, 13, 12.
The highest frequency is 17.
Find the mark corresponding to the highest frequency.
The mark corresponding to the frequency 17 is 4.
Therefore, the modal mark is 4.

The correct option is B.
$\boxed{\text{B. 4}}$
20. If a student is selected at random, what is the probability that the student obtained at most 7 marks?

"At most 7 marks" means the student obtained a mark of 7 or less (i.e., marks 1, 2, 3, 4, 5, 6, or 7).
Calculate the number of students who obtained at most 7 marks.
$\text{Number of students (marks} \le 7) = 11 + 12 + 10 + 17 + 16 + 15 + 14$ $\text{Number of students (marks} \le 7) = 95$
Determine the total number of students.
From question 18, the total number of students is $\sum f = 120$ .
Calculate the probability.
$\text{Probability} = \frac{\text{Number of students (marks} \le 7)}{\text{Total number of students}}$ $\text{Probability} = \frac{95}{120}$
Simplify the fraction.
Both the numerator and the denominator are divisible by 5.
$\text{Probability} = \frac{95 \div 5}{120 \div 5} = \frac{19}{24}$
The correct option is A.
$\boxed{\text{A. } \frac{19}{24}}$

What is the mean mark?

Answer

Step-by-step solution

18. What is the mean mark?

Calculate the sum of (frequency $\times$ mark), $\sum (f \times x)$ .

Calculate the total number of students, $\sum f$ .

Calculate the mean mark.

19. What is the modal mark?

Identify the highest frequency from the "No. of students" row.

Find the mark corresponding to the highest frequency.

20. If a student is selected at random, what is the probability that the student obtained at most 7 marks?

Calculate the number of students who obtained at most 7 marks.

Determine the total number of students.

Calculate the probability.

Simplify the fraction.

Try one yourself

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What is the mean mark?

Answer

Step-by-step solution

18. What is the mean mark?

Calculate the sum of (frequency ×\times× mark), ∑(f×x)\sum (f \times x)∑(f×x).

Calculate the total number of students, ∑f\sum f∑f.

Calculate the mean mark.

19. What is the modal mark?

Identify the highest frequency from the "No. of students" row.

Find the mark corresponding to the highest frequency.

20. If a student is selected at random, what is the probability that the student obtained at most 7 marks?

Calculate the number of students who obtained at most 7 marks.

Determine the total number of students.

Calculate the probability.

Simplify the fraction.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Calculate the sum of (frequency $\times$ mark), $\sum (f \times x)$ .

Calculate the total number of students, $\sum f$ .