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Let's analyze the data and solve the questions step by step.

### Data Provided
The marks are:
\[ 62, 76, 94, 69, 89, 85, 71, 97, 86, 64, 80, 63, 75, 85 \]

### a) List the data in order from smallest to largest
We first arrange the data in ascending order:

\[ 62, 63, 64, 69, 71, 75, 76, 80, 85, 85, 86, 89, 94, 97 \]

### b) Find:

#### i) The minimum value
The minimum value is the smallest number in the ordered list.
\[ \text{Minimum value} = 62 \]

#### ii) The maximum value
The maximum value is the largest number in the ordered list.
\[ \text{Maximum value} = 97 \]

#### iii) The range
The range is the difference between the maximum and minimum values.
\[ \text{Range} = 97 - 62 = 35 \]

#### iv) The median (Q2)
The median is the middle value in the ordered list. Since there are 14 data points, the median will be the average of the 7th and 8th values.

7th value: 76  
8th value: 80

\[ \text{Median (Q2)} = \frac{76 + 80}{2} = \frac{156}{2} = 78 \]

#### v) The lower quartile (Q1)
The lower quartile (Q1) is the median of the lower half of the data. For the first 7 numbers:

\[ 62, 63, 64, 69, 71, 75, 76 \]

The median of these is the 4th value (69).

\[ \text{Lower quartile (Q1)} = 69 \]

#### vi) The upper quartile (Q3)
The upper quartile (Q3) is the median of the upper half of the data. For the last 7 numbers:

\[ 80, 85, 85, 86, 89, 94, 97 \]

The median of these is the 4th value (86).

\[ \text{Upper quartile (Q3)} = 86 \]

### Final Answers
1. **Minimum value**: 62
2. **Maximum value**: 97
3. **Range**: 35
4. **Median (Q2)**: 78
5. **Lower quartile (Q1)**: 69
6. **Upper quartile (Q3)**: 86

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Would you like further details or explanations on any of these steps? Here are some related questions to practice:

1. What would the range be if the maximum value was 99 instead of 97?
2. How would the median change if there was an additional score of 83 added to the data?
3. Can you identify any outliers in this data set?
4. What is the interquartile range (IQR) for this data set?
5. How would you calculate the mean of the data set?

**Tip:** When calculating the median, always ensure the data is ordered from smallest to largest, and double-check the number of data points to determine whether you should average two middle values or not.

The data below shows the mark out of 100 on a Statistics test for a group of Year 9 students. List the data in order from smallest to largest and find: i) the minimum value ii) the maximum value iii) the range iv) the median (Q2) v) the lower quartile (Q1) vi) the upper quartile (Q3).

Analyze a set of marks from a Statistics test and learn how to calculate the minimum, maximum, range, median (Q2), lower quartile (Q1), and upper quartile (Q3) for a group of Year 9 students. Step-by-step solution provided, including ordering the data and using key statistical formulas.

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