The table shows the distribution of marks scored by some students in an aptitude test. (i) Find the: I. mode…

Question

The table shows the distribution of marks scored by some students in an aptitude test. (i) Find the: I. mode; II. range of the distribution. (ii) Calculate correct to three significant figures, the mean mark.

ScanSolve AI Tutor · Accepted Answer

Here's the solution for the distribution of marks:

a)

(i) I. Mode

Identify the mark with the highest frequency.
From the table, the highest frequency is 24, which corresponds to the mark of 45.
The mode is $\boxed{\text{45}}$ .

(i) II. Range of the distribution
Identify the highest and lowest marks.
Highest mark = 75
Lowest mark = 15
Calculate the range.
$\text{Range} = \text{Highest mark} - \text{Lowest mark}$ $\text{Range} = 75 - 15$ $\text{Range} = 60$
The range is $\boxed{\text{60}}$ .

(ii) Calculate correct to three significant figures, the mean mark.
Calculate the total frequency ( $\sum f$ ).
$\sum f = 1 + 4 + 12 + 24 + 18 + 8 + 3$ $\sum f = 70$
Calculate the sum of (mark $\times$ frequency) ( $\sum fx$ ).
$\sum fx = (15 \times 1) + (25 \times 4) + (35 \times 12) + (45 \times 24) + (55 \times 18) + (65 \times 8) + (75 \times 3)$ $\sum fx = 15 + 100 + 420 + 1080 + 990 + 520 + 225$ $\sum fx = 3350$
Calculate the mean ( $\bar{x}$ ) using the formula $\bar{x} = \frac{\sum fx}{\sum f}$ .
$\bar{x} = \frac{3350}{70}$ $\bar{x} \approx 47.85714...$
Round the mean to three significant figures.
$\bar{x} \approx 47.9$
The mean mark is $\boxed{\text{47.9}}$ .

The table shows the distribution of marks scored by some students in an aptitude test. (i) Find the: I. mode; II. range of the distribution. (ii) Calculate correct to three significant figures, the mean mark.

Step-by-step solution

Identify the mark with the highest frequency.

Identify the highest and lowest marks.

Calculate the range.

Calculate the total frequency ( $\sum f$ ).

Calculate the sum of (mark $\times$ frequency) ( $\sum fx$ ).

Calculate the mean ( $\bar{x}$ ) using the formula $\bar{x} = \frac{\sum fx}{\sum f}$ .

Round the mean to three significant figures.

Still stuck on this one?

More Mathematics Questions

The table shows the distribution of marks scored by some students in an aptitude test. (i) Find the: I. mode; II. range of the distribution. (ii) Calculate correct to three significant figures, the mean mark.

Step-by-step solution

Identify the mark with the highest frequency.

Identify the highest and lowest marks.

Calculate the range.

Calculate the total frequency (∑f\sum f∑f).

Calculate the sum of (mark ×\times× frequency) (∑fx\sum fx∑fx).

Calculate the mean (xˉ\bar{x}xˉ) using the formula xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}xˉ=∑f∑fx​.

Round the mean to three significant figures.

Still stuck on this one?

More Mathematics Questions

Calculate the total frequency ( $\sum f$ ).

Calculate the sum of (mark $\times$ frequency) ( $\sum fx$ ).

Calculate the mean ( $\bar{x}$ ) using the formula $\bar{x} = \frac{\sum fx}{\sum f}$ .