Grade 12 Mathematical Literacy — Data Handling Exam Quiz

Is the data in Table 2 discrete or continuous? Give a reason.

1. Discrete — the ages are counted in whole years, so only certain values are possible
2. Continuous — age can be measured to any level of accuracy
3. Discrete — because there are only 19 children
4. Continuous — because the ages are all different

Answer: Discrete — the ages are counted in whole years, so only certain values are possible

\(\text{The ages were RECORDED as whole numbers, so they are counted, not measured.}\)

\(\text{Counted data} = \text{discrete.}\)

*\(\text{The reason earns the second mark — never give a one-word answer.}\)

Name one method Mrs Smith could have used to collect this data.

1. Observation — she recorded the children as they attended
2. A tally of every household in the town
3. A newspaper article about swimming
4. An estimate based on last year's figures

Answer: Observation — she recorded the children as they attended

\(\text{She 'kept the record' of children who participated — she watched and recorded.}\)

*\(\text{A questionnaire or interview would also be accepted if justified.}\)

Determine the median age.

1. 13
2. 13,21
3. 12
4. 14

Answer: 13

\(\text{Order the 19 ages: } 8;9;10;10;10;11;12;12;13;\mathbf{13};13;14;14;15;15;16;17;17;17;18\)

\(\text{Position} = \dfrac{19+1}{2} = 10\text{th value}\)

Calculate the range of the ages.

1. 10
2. 26
3. 8
4. 18

Answer: 10

\(\text{Range} = \text{maximum} - \text{minimum}\)

\(= 18 - 8\)

Determine the mean age (correct to two decimal places).

1. 13,21
2. 13,00
3. 12,55
4. 14,50

Answer: 13,21

\(\text{Sum of all ages} = 251\)

\(\text{Mean} = \dfrac{251}{19} = 13{,}2105\ldots\)