Mean, Median, Mode Notes and Worksheets - Lindsay Bowden - Free Printable

Problem: Measures of Central Tendency Review Practice 2

#### Instructions: Answer each question on measures of central tendency.

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Solution and Explanation

#### 1. Explain how to determine if you should use mean or median.
- Mean: The mean is the average of all the numbers in a data set. It is calculated by summing all the values and dividing by the number of values.
- Median: The median is the middle value when the data set is ordered from least to greatest. If there is an even number of values, the median is the average of the two middle numbers.

When to Use Mean:
- Use the mean when the data set does not have extreme outliers (very high or very low values) because the mean is sensitive to these outliers.
- The mean is appropriate for symmetric distributions where most values cluster around the center.

When to Use Median:
- Use the median when the data set has outliers or is skewed (not symmetric). The median is less affected by extreme values.
- The median is useful for ordinal data or when you want a measure that represents the "middle" value.

Summary:
- Use the mean for symmetric data without outliers.
- Use the median for skewed data or data with outliers.

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#### 2. True or False: A data set can have more than one mode.
- Mode: The mode is the value that appears most frequently in a data set.
- A data set can indeed have more than one mode. For example, in the data set {2, 3, 3, 4, 4}, both 3 and 4 appear twice, making them both modes. This is called a bimodal distribution.

Answer: True

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#### 3. Would mean, median, or mode be most appropriate for this data set:
- Data set: 373, 346, 387, 105, 397, 299, 357, 343, 368

To determine the most appropriate measure:
1. Check for Outliers: The value 105 is significantly lower than the other values, which suggests it might be an outlier.
2. Symmetry: The data set appears to be somewhat skewed due to the presence of the outlier.
3. Appropriate Measure: Since there is an outlier, the median is more appropriate because it is less affected by extreme values.

Answer: Median

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#### 4. Gina put a set of numbers in order from least to greatest. Then she found the number that occurred the most frequently. Which measure of central tendency did she find?
- When Gina ordered the numbers and found the one that occurred most frequently, she was identifying the mode.

Answer: Mode

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#### 5. Manuel surveyed his classmates about their favorite pet. These are the results: cat, dog, cat, rabbit, guinea pig, dog, fish, turtle, cat. Which measure of central tendency should he use for this data set?
- This is a categorical data set (types of pets), so the mode is the most appropriate measure. The mode tells us the most common category (favorite pet).

Answer: Mode

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#### 6. A meteorologist measured how many inches of snow and city got each day for 12 days. He recorded: 2", 0", 1", 1", 3", 4", 0", 0", 1", 2", 0". Which measure of central tendency would most appropriate for this data set?
- This is a numerical data set with some zeros (no snowfall). There are no extreme outliers, and the data appears relatively symmetric.
- The mean would be appropriate here because it takes into account all the values, including the zeros, and provides an overall average.

Answer: Mean

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#### 7. True or False: A data set can have more than one mean.
- The mean is a single value calculated by summing all the numbers and dividing by the count. A data set cannot have more than one mean.

Answer: False

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#### 8. Joanna ordered a data set from least to greatest. Then she found the two middle numbers, added them, and divided by 2. Which measure of central tendency did she find?
- When Joanna ordered the data set and found the average of the two middle numbers, she was calculating the median.

Answer: Median

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#### 9. Real-life application: Ask 7 classmates how many siblings they have. Record their answers below.
- Suppose the responses are: 2, 1, 0, 3, 2, 1, 2.

#### 10. Find the mean, median, and mode of the data set.
- Data Set: 2, 1, 0, 3, 2, 1, 2

1. Mean:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{2 + 1 + 0 + 3 + 2 + 1 + 2}{7} = \frac{11}{7} \approx 1.57
\]

2. Median:
- Order the data: