Q1. Find the mean, median, mode, and range for the golf scores: 71, 67, 67, 72, 76, 72, 73, 68, 72, 72

Background

Topic: Descriptive Statistics

This question tests your ability to calculate measures of central tendency (mean, median, mode) and dispersion (range) for a data set.

Key Terms and Formulas:

• Mean:

• Median: The middle value when data is ordered

• Mode: The value(s) that appear most frequently

• Range:

Step-by-Step Guidance

1. Order the scores from least to greatest.

2. Calculate the mean by adding all scores and dividing by the number of scores.

3. Find the median by locating the middle value(s) in the ordered list.

4. Identify the mode by finding the score(s) that occur most often.

5. Determine the range by subtracting the lowest score from the highest score.

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Q2. Find the sample standard deviation, variance, quartiles, and outliers for: 22, 29, 21, 24, 27, 28, 25, 36

Background

Topic: Descriptive Statistics – Measures of Spread and Position

This question tests your ability to compute standard deviation, variance, quartiles, and identify outliers in a data set.

Key Terms and Formulas:

• Sample Variance:

• Sample Standard Deviation:

• Quartiles: Q1, Q2 (median), Q3

• Outliers: Values outside

• Interquartile Range (IQR):

Step-by-Step Guidance

1. Order the data from smallest to largest.

2. Calculate the mean () of the data.

3. Compute the variance using the formula above.

4. Find the standard deviation by taking the square root of the variance.

5. Determine Q1, Q2, and Q3 by splitting the ordered data into quartiles.

6. Calculate the IQR and check for outliers using the outlier formula.

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Q3. Display the data below in a stem-and-leaf plot.

Background

Topic: Data Visualization – Stem-and-Leaf Plot

This question tests your ability to organize and display data using a stem-and-leaf plot, which shows the distribution and shape of the data.

Key Terms:

• Stem-and-Leaf Plot: A method of displaying quantitative data where each data value is split into a "stem" (leading digit(s)) and a "leaf" (trailing digit).

Step-by-Step Guidance

1. Identify the stems (usually the tens place) and leaves (ones place) for each data value.

2. Organize the data by listing stems in order and placing leaves next to their corresponding stem.

3. Check that all data values are included and the plot is properly formatted.

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Q4. Draw a box-and-whisker plot for the test scores of 30 students and approximate the mean and standard deviation of the grouped data.

Background

Topic: Data Visualization and Grouped Data Statistics

This question tests your ability to create a box-and-whisker plot (boxplot) and estimate the mean and standard deviation for grouped data.

Key Terms and Formulas:

• Box-and-Whisker Plot: Visualizes the five-number summary (minimum, Q1, median, Q3, maximum).

• Grouped Data Mean: , where is frequency and is midpoint.

• Grouped Data Standard Deviation:

Step-by-Step Guidance

1. Order the test scores and identify the five-number summary (min, Q1, median, Q3, max).

2. Draw the boxplot using these values.

3. For grouped data, calculate the midpoint for each class interval.

4. Multiply each midpoint by its frequency and sum these products.

5. Divide by the total frequency to estimate the mean.

6. Use the formula for grouped data standard deviation, but stop before the final calculation.

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Q5. Approximate the mean and standard deviation for the grouped height data:

Background

Topic: Grouped Data Statistics

This question tests your ability to estimate the mean and standard deviation from frequency distributions.

Key Terms and Formulas:

• Mean for grouped data:

• Standard deviation for grouped data:

• = frequency, = midpoint of each class

Step-by-Step Guidance

1. Find the midpoint for each class interval.

2. Multiply each midpoint by its frequency and sum the results.

3. Divide by the total frequency to estimate the mean.

4. Calculate for each class, multiply by frequency, and sum.

5. Divide by the total frequency and take the square root to estimate the standard deviation.

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