## Problem solving

 8.3 Problem Solving

 SITUATION 1

A group of 15 pupils received school shoes sponsored by the Parent-Teacher Association (PTA) of the school. The number of pupils that received sizes 3 and 4 shoes are 4 pupils and 6 pupils respectively. Size 5 shoes were given to 3 pupils and the rest received size 6 shoes.

Find the mode, range, median, mean.

 SIZE Number of Pupils 3 4 4 6 5 3 6 2

MODE:
The highest frequency is 6.
Therefore, the mode is size 4.

RANGE:
Range = Maximum value - Minimum value
= 6 - 3
= 3
The range of the shoe size is 3.

MEDIAN:
There are 15 pieces of data. Median is the value of the data that is in the middle.

3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6

Therefore, the median is size 4.

MEAN:
4 x 3 = 12

6 x 4 = 24

3 x 5 = 15

2 x 6 = 12

$$\text{Mean} = \dfrac{12+24+15+12}{15}\\ \quad\quad\quad=\dfrac{63}{15}\\ \quad\quad\quad=4.2$$

The mean is size 4.2.

 SITUATION 2

The two bar charts show the scores of 10 boys and 10 girls in the athletic events of the 1 Malaysia Sports Camp.

Find the mode, range, median and mean for the boys' and girls' scores.

SOLUTION:

 MODE

 BOYS' SCORE GIRLS' SCORE The highest frequency is 3 boys. The boys' mode is score 12. The highest frequency is 4 girls. The girls' mode is score 15.

 RANGE

 BOYS' SCORE GIRLS' SCORE Range = Maximum value - Minimum value Range = 20 - 4 = 16 The boys' range is score 16. Range = Maximum value - Minimum value Range = 20 - 5 = 15        The girls' range is score 15.

 MEDIAN

 BOYS' SCORE GIRLS' SCORE Boys' median: 4, 8, 8, 12, 12, 12, 16, 16, 20, 20 $$\text{Median}= \dfrac{12 + 12}{2}=12$$ The boys' median is score 12. Girls' median: 5, 10, 10, 10, 15, 15, 15, 15, 20, 20 $$\text{Median}= \dfrac{15 + 15}{2}=15$$ The girls' median is score 15.

 MEAN

 BOYS' SCORE GIRLS' SCORE 1 x 4 = 4 2 x 8 = 16 3 x 12 = 36 2 x 16 = 32 2 x 20 = 40 $$\text{Min} = \dfrac{4+16+36+32+40}{10}=12.8$$ The boys' mean is 12.8. 1 x 5 = 5 3 x 10 = 30 4 x 15 = 60 2 x 20 = 40   $$\text{Min} = \dfrac{5+30+60+40}{10}=13.5$$ The girls' mean is 13.5.