Let's break down each part of the problem:

Question 17

You are asked to use the box-and-whisker plots for the following parts.

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(a) What is the median score for Miss Lee's class?

The median score is represented by the middle line inside the box of the box-and-whisker plot for Miss Lee’s class. Read the value from the plot.

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(b) Complete the statement:

About 25% of all students scored higher than _______ in Miss Singh's class.

In a box plot, 25% of the data lies above the upper quartile (the right edge of the box). Find this value for Miss Singh's class from the plot.

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(c) Find the IQR for Miss Lee's class.

The Interquartile Range (IQR) is calculated as: $\text{IQR} = Q3 - Q1$ Where $Q1$ is the lower quartile and $Q3$ is the upper quartile. Find these values from Miss Lee's class plot and calculate the difference.

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(d) Complete the statement:

The median score in Miss Lee's class is the same as the _______ score in Miss Singh's class.

Here, you'll compare the median score from Miss Lee’s class with the five-number summary values (minimum, lower quartile, median, upper quartile, maximum) from Miss Singh’s class and fill in the blank accordingly.

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Question 18

(a) List the five-number summary

The five-number summary includes:

1. Minimum: The smallest value in the dataset.
2. Lower Quartile (Q1): The 25th percentile.
3. Median: The 50th percentile.
4. Upper Quartile (Q3): The 75th percentile.
5. Maximum: The largest value in the dataset.

These values can be read directly from the box plot.

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(b) Assuming there are 500 data values in the sample, approximately how many values would fall between 1 and 2?

Look at the portion of the box plot that lies between 1 and 2. Determine the percentage of data in that range and apply it to the total of 500 values: $\text{Number of values} = \left(\frac{\text{Percentage of values}}{100}\right) \times 500$ Round to the nearest whole number.

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(c) Approximately what percentage of the data falls below 7, and what percentage lies above 7?

From the box plot, identify the proportion of data below and above the value of 7. Box plots divide the data into quartiles, so you can estimate these percentages.

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Question 19

You are given a dataset of highway mileage for five different car models: $21, 23, 26, 28, 28, 30$ You need to compute the following:

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(a) Mean

The mean is calculated by taking the sum of all the values and dividing by the number of values: $\text{Mean} = \frac{21 + 23 + 26 + 28 + 28 + 30}{6}$

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(b) Median

The median is the middle value in a dataset when the numbers are arranged in order. If the dataset has an even number of values, it is the average of the two middle numbers.

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(c) Mode

The mode is the value that appears most frequently in the dataset.

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(d) Midrange

The midrange is calculated by averaging the minimum and maximum values: $\text{Midrange} = \frac{\text{Min} + \text{Max}}{2}$

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Would you like to go through any part in more detail?

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Here are 5 relative questions:

1. How does the IQR help in understanding the spread of the data in Miss Lee's class?
2. What does it mean when the median and quartiles are close together in a box plot?
3. How can we use box-and-whisker plots to compare the variability between two classes?
4. How does knowing the percentage of data in different sections of the plot help in data analysis?
5. What would you infer about a dataset if the midrange and median are close together?

Tip: When analyzing a box plot, always check for symmetry or skewness as it provides insights into the distribution of data.