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QUESTION 3

Lisa's younger sister is a learner at Plime Secondary School. She is taking her subject and decided to compare the performance in both Paper 1 and Paper 2 of the June examination. The marks for each paper are displayed below:

Mathematical Literacy Paper 1:
[tex]\[
\begin{array}{l}
120, 118, 115, 114, 87, 94, 113, 104, 113, 96, 105, 119, 120, 109
\end{array}
\][/tex]

Mathematical Literacy Paper 2:
[tex]\[
\begin{array}{l}
107, 115, 104, 83, 61, 100, 104, M, 113, 120, 108, 126, 124, 105
\end{array}
\][/tex]

a) Calculate the mean mark for Paper 1.

b) If the paper was out of 150, what was the percentage mean for Paper 1?

c) Find the value of [tex]\(M\)[/tex], if the range of the data is 77.

Hatuli, Bianca, and Khotso wrote some practice tests at their school. Their scores are given in the table below:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
& 4 & 6 & 80 & 48 & 5 & 7 & 48 & 70 & 86 \\
\hline
3 & 4 & 4 & 58 & 60 & 6 & 5 & 76 & 80 & \\
\hline
6 & 2 & 8 & & & 8 & 2 & & & \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's tackle the question step-by-step.

### Step 1: Calculate the mean mark for Paper 1
The marks for Mathematical Literacy Paper 1 are:
[tex]\[ 120, 118, 115, 114, 87, 94, 113, 104, 113, 96, 105, 119, 120, 109 \][/tex]

To find the mean mark:
1. Sum all the marks.
2. Divide by the number of marks.

Sum of marks:
[tex]\[ 120 + 118 + 115 + 114 + 87 + 94 + 113 + 104 + 113 + 96 + 105 + 119 + 120 + 109 = 1527 \][/tex]

Number of marks:
[tex]\[ 14 \][/tex]

Mean mark for Paper 1:
[tex]\[ \text{Mean} = \frac{1527}{14} = 109.07142857142857 \][/tex]

### Step 2: Calculate the percentage mean for Paper 1
Since the paper was out of 150, the percentage mean is calculated as follows:
[tex]\[ \text{Percentage Mean} = \left( \frac{\text{Mean}}{150} \right) \times 100 \][/tex]

Substitute the calculated mean:
[tex]\[ \text{Percentage Mean} = \left( \frac{109.07142857142857}{150} \right) \times 100 = 72.71428571428571\% \][/tex]

### Step 3: Find the value of [tex]\( M \)[/tex]
The marks for Mathematical Literacy Paper 2 are:
[tex]\[ 107, 115, 104, 83, 61, 100, 104, M, 113, 120, 108, 126, 124, 105 \][/tex]

The range of a data set is the difference between the maximum and minimum values. Given the data, the known maximum and minimum values in Paper 2 are:
[tex]\[ \max_{\text{without } M} = 126 \][/tex]
[tex]\[ \min_{\text{without } M} = 61 \][/tex]
[tex]\[ \text{Observed range without } M = 126 - 61 = 65 \][/tex]

We are given that the range should be 77.
Thus, let's calculate the additional range needed:
[tex]\[ \text{Additional range} = 77 - 65 = 12 \][/tex]

Therefore, [tex]\( M \)[/tex] should be:
[tex]\[ M = \max_{\text{without } M} + \text{Additional range} \][/tex]
[tex]\[ M = 126 + 12 = 138 \][/tex]

So, the value of [tex]\( M \)[/tex] is 138.

### Summary
1. The mean mark for Paper 1 is [tex]\( 109.07142857142857 \)[/tex].
2. The percentage mean for Paper 1, if the paper was out of 150, is [tex]\( 72.71428571428571\% \)[/tex].
3. The value of [tex]\( M \)[/tex] in Paper 2, given that the range is 77, is [tex]\( 138 \)[/tex].

I hope this helps you understand how we arrived at the answers! If you have any further questions, feel free to ask.
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