# Math Help - Math Help

1. ## Math Help

These are probably simple for most of you but im not really good in math and I dont have any idea on how to solve these questions.

1. Use technology to calculate the mean, median, and mode for the following data sets.

a) Marks on a set of tests ( 66,65,72,78, 93, 70, 68, 64) (Answered)

2. Hakim's Shoes reported the following sale results:
Size 1 5 6 7 8 9 10
Frequency 5 11 15 18 19 13 7

a) Calculate the mean media and mode shoe size. (Answered)
b) Which measure of central tendency is most appropriate? Why?

3. The mean of one class in 65 and the mean of another class is 75. Explain the steps you would need to take to calculate a combined class average.

4. A student term mark is 75. The term mark counts for 70% of the final mark. What mark must the student achieve on the exam to earn a final mark of
a) at least 70? b)75? c) 85 (choose one option).

Posted in the wrong section XD can someone please move it.

2. Originally Posted by Skoz
These are probably simple for most of you but im not really good in math and I dont have any idea on how to solve these questions.

1. Use technology to calculate the mean, median, and mode for the following data sets.

a) Marks on a set of tests ( 66,65,72,78, 93, 70, 68, 64)

2. Hakim's Shoes reported the following sale results:
Size 1 5 6 7 8 9 10
Frequency 5 11 15 18 19 13 7

a) Calculate the mean media and mode shoe size.
b) Which measure of central tendency is most appropriate? Why?

3. The mean of one class in 65 and the mean of another class is 75. Explain the steps you would need to take to calculate a combined class average.

4. A student term mark is 75. The term mark counts for 70% of the final mark. What mark must the student achieve on the exam to earn a final mark of
a) at least 70? b)75? c) 85 (choose one option).

Posted in the wrong section XD can someone please move it.
(a) $Mean = \frac {sum \;of\; all\; values}{number \;of \;values.}$

$mean= \frac{66+65+72+78+93+70+68+64}{8}$

$= \frac{576}{8}$

$= 72$

For median, Arrange all the values in a order (increasing or decreasing order)
64, 65, 66, 68, 70,72,78,93

There are two mid values, 68 and 70

Median $=\frac{68+70}{2}$

= 69

Mode is the value which occurs maximum number of times. There is no such value here. All of them occur only once. So it does not have any mode.

3. Thank you so much you make it so simple .

4. 3. The mean of one class in 65 and the mean of another class is 75. Explain the steps you would need to take to calculate a combined class average.

Please see,
Let number of students in first class $=n_1$

Let number of students in second class $=n_2$

Total Sum for first class $= 65\times n_1$

Total Sum for second class $= 75\times n_2$

combined class average $=\frac {65\times n_1 +75 \times n_2}{n_1 + n_2}$

$=\frac {65 n_1 +75 n_2}{n_1 + n_2}$

5. 4. A student term mark is 75. The term mark counts for 70% of the final mark. What mark must the student achieve on the exam to earn a final mark of
a) at least 70? b)75? c) 85 (choose one option).

Posted in the wrong section XD can someone please move it.[/quote]
Let us assume mean marks for first test $\overline {x_1 }=75$ and its weightage $=w_1$= 70% = 0.7

Let us assume mean marks for second test $=\overline {x_2 }$ and its weightage $=w_2$ = 100% - 70% = 1- 0.7= 0.3

(a) The final weighted mean =

$
\overline {x_w } = \frac{{\overline {x_1 } \times w_1 + \overline {x_2 } \times w_2 }}
{{w{}_1 + w_2 }} \hfill \\$

$\frac{{75 \times 0.7 + \overline {x_2 } \times 0.3}}
{{0.7 + 0.3}} \geqslant 70 \hfill \\$

$52.5 + 0.3\overline {x_2 } \geqslant 70 \hfill \\$

$0.3\overline {x_2 } \geqslant 70 - 52.5 \hfill \\$

$0.3\overline {x_2 } \geqslant 17.5 \hfill \\$

$\overline {x_2 } \geqslant \frac{17.5}
{0.3}$

$\overline {x_2 } \geqslant 58.33 \hfill \\$

$\overline {x_2 } = 59{\text{ or more marks}}{\text{.}} \hfill \\$

He should get 59 or more marks in second exam to make it at least 70 final score.

(b)The final weighted mean =

$
\overline {x_w } = \frac{{\overline {x_1 } \times w_1 + \overline {x_2 } \times w_2 }}
{{w{}_1 + w_2 }} \hfill \\$

$\frac{{75 \times 0.7 + \overline {x_2 } \times 0.3}}
{{0.7 + 0.3}} = 75 \hfill \\$

$52.5 + 0.3\overline {x_2 } = 75 \hfill \\$

$0.3\overline {x_2 } = 75 - 52.5 \hfill \\$

$0.3\overline {x_2 } = 22.5 \hfill \\$

$\overline {x_2 } = \frac{22.5}{0.3}$

$\overline {x_2 } =75\hfill \\$

He should get 75 marks in the second exam.

(c) The final weighted mean =

$
\overline {x_w } = \frac{{\overline {x_1 } \times w_1 + \overline {x_2 } \times w_2 }}
{{w{}_1 + w_2 }} \hfill \\$

$\frac{{75 \times 0.7 + \overline {x_2 } \times 0.3}}
{{0.7 + 0.3}} = 85 \hfill \\$

$52.5 + 0.3\overline {x_2 } = 85 \hfill \\$

$0.3\overline {x_2 } = 85 - 52.5 \hfill \\$

$0.3\overline {x_2 } = 32.5 \hfill \\$

$\overline {x_2 } = \frac{32.5}{0.3}$

$\overline {x_2 } =108.33\hfill \\$

$\overline {x_2 } = 109\hfill \\$

He should get 109 marks in second exam to make final score of 85.