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(12 marks)

Table 2.2: Scores of candidates

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Marks (6) & [tex]$1-10$[/tex] & [tex]$11-20$[/tex] & [tex]$21-30$[/tex] & [tex]$31-40$[/tex] & [tex]$41-50$[/tex] & [tex]$51-60$[/tex] \\
\hline
Frequency & 8 & 36 & 38 & 30 & 15 & 5 \\
\hline
\end{tabular}

(a) From Table 2.2, calculate, correct to one decimal place, the:
1. Mean score
2. Median score
3. Modal score



Answer :

GinnyAnswer
### Solution:
Let's calculate the different statistical measures (mean score, median score, and modal score) from the given data.

#### (i) Mean Score:
The mean score is the average of all the scores. To find it, add all the scores together and then divide by the number of scores.

Scores Provided: 36, 38, 30, 15, 5

1. Calculate the sum of the scores:
[tex]\[ 36 + 38 + 30 + 15 + 5 = 124 \][/tex]

2. Divide the sum by the number of scores (which is 5 in this case):
[tex]\[ \text{Mean score} = \frac{124}{5} = 24.8 \][/tex]

So, the mean score, correct to one decimal place, is 24.8.

#### (ii) Median Score:
The median score is the middle score when all the scores are arranged in ascending order.

1. First, sort the scores in ascending order:
[tex]\[ 5, 15, 30, 36, 38 \][/tex]

2. Since there is an odd number of scores (5 scores), the median is the middle score:
[tex]\[ \text{Median score} = 30 \][/tex]

So, the median score is 30.

#### (iii) Modal Score:
The modal score is the score that appears most frequently in the data set.

1. Count the frequency of each score:
- 36 appears 1 time
- 38 appears 1 time
- 30 appears 1 time
- 15 appears 1 time
- 5 appears 1 time

2. Determine the score with the highest frequency:
- Since each score appears only once, we check the highest individual score.

The modal score, in this case, is the highest unique score, which is 36.

### Summary of Calculated Scores:
- Mean score: 24.8
- Median score: 30
- Modal score: 36

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