The following is record of scores obtained 30 J.H.S. 2 pupils in a test marked out of 5: 5, 4, 3, 1, 3, 3, 4…

Question

The following is record of scores obtained 30 J.H.S. 2 pupils in a test marked out of 5: 5, 4, 3, 1, 3, 3, 4, 2, 3, 4, 3, 1 2, 3, 3, 2, 1 A. Construct a frequency table for the data. B. Find the median marks. C. Calculate the mean of the distribution

ScanSolve AI Tutor · Accepted Answer

The problem states "30 J.H.S. 2 pupils" but only 19 scores are provided in the data. We will proceed with the 19 given scores.

The given scores are:
$5, 3, 2, 4, 5, 2, 3, 3, 4, 2, 1, 3, 3, 4, 2, 3, 4, 3, 1$

A) Construct a frequency table for the data.

Count the frequency of each score.
- Score 1: Appears 2 times
- Score 2: Appears 4 times
- Score 3: Appears 7 times
- Score 4: Appears 4 times
- Score 5: Appears 2 times The total number of scores is $2+4+7+4+2 = 19$ .
Create the frequency table.
$\begin{array}{|c|c|} \hline \textbf{Score (x)} & \textbf{Frequency (f)} \\ \hline 1 & 2 \\ 2 & 4 \\ 3 & 7 \\ 4 & 4 \\ 5 & 2 \\ \hline \textbf{Total} & \textbf{19} \\ \hline \end{array}$
The frequency table is shown above.

B) Find the median marks.
Determine the position of the median.
Since the total number of scores ( $N$ ) is 19 (an odd number), the median is the value at the $\frac{N+1}{2}$ position.
$\text{Median position} = \frac{19+1}{2} = \frac{20}{2} = 10^{\text{th}}$
The median is the 10th score when the data is arranged in ascending order.
Find the 10th score.
Let's list the scores in ascending order using the frequency table:
$1, 1$ (2 scores)
$2, 2, 2, 2$ (next 4 scores, cumulative total: $2+4=6$ scores)
$3, 3, 3, 3, 3, 3, 3$ (next 7 scores, cumulative total: $6+7=13$ scores)
The 10th score falls within the group of scores that are 3. Specifically, the 7th score is 3, the 8th is 3, the 9th is 3, and the 10th score is 3.

The median mark is $\boxed{\textbf{3}}$ .

C) Calculate the mean of the distribution.
Calculate the sum of (score $\times$ frequency) for all scores.
We add an $fx$ column to the frequency table:
$\begin{array}{|c|c|c|} \hline \textbf{Score (x)} & \textbf{Frequency (f)} & \textbf{fx} \\ \hline 1 & 2 & 1 \times 2 = 2 \\ 2 & 4 & 2 \times 4 = 8 \\ 3 & 7 & 3 \times 7 = 21 \\ 4 & 4 & 4 \times 4 = 16 \\ 5 & 2 & 5 \times 2 = 10 \\ \hline \textbf{Total} & \sum f = 19 & \sum fx = 2+8+21+16+10 = 57 \\ \hline \end{array}$
Calculate the mean using the formula $\bar{x} = \frac{\sum fx}{\sum f}$ .
$\bar{x} = \frac{57}{19}$ $\bar{x} = 3$
The mean of the distribution is $\boxed{\textbf{3}}$ .

The following is record of scores obtained 30 J.H.S. 2 pupils in a test marked out of 5: 5, 4, 3, 1, 3, 3, 4, 2, 3, 4, 3, 1 2, 3, 3, 2, 1 A. Construct a frequency table for the data. B. Find the median marks. C. Calculate the mean of the distribution

Step-by-step solution

Count the frequency of each score.

Create the frequency table.

Determine the position of the median.

Find the 10th score.

Calculate the sum of (score $\times$ frequency) for all scores.

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

Still stuck on this one?

More Mathematics Questions

The following is record of scores obtained 30 J.H.S. 2 pupils in a test marked out of 5: 5, 4, 3, 1, 3, 3, 4, 2, 3, 4, 3, 1 2, 3, 3, 2, 1 A. Construct a frequency table for the data. B. Find the median marks. C. Calculate the mean of the distribution

Step-by-step solution

Count the frequency of each score.

Create the frequency table.

Determine the position of the median.

Find the 10th score.

Calculate the sum of (score ×\times× frequency) for all scores.

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

Still stuck on this one?

More Mathematics Questions

Calculate the sum of (score $\times$ frequency) for all scores.

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