7.3.1 Statistical Methods

• How is the mean calculated in descriptive statistics?

  Sum values / total number
• What is the mode in descriptive statistics?

  Most frequent value
• What is the standard deviation in descriptive statistics?

  Square root of variance
• Measures of central tendency describe the typical value in a data set.


  True
• Measures of dispersion describe how spread out the data is.


  True
• Match the descriptive statistic with its description:

  Mean ↔️ The average value

  Median ↔️ The middle value in order

  Mode ↔️ The most frequent value

  Range ↔️ Difference between highest and lowest
• Inferential statistics summarize the key features of a data set.

  False
• Steps in hypothesis testing

  1️⃣ State null and alternative hypotheses

  2️⃣ Choose a significance level

  3️⃣ Calculate the test statistic

  4️⃣ Compare test statistic to critical value
• What is the purpose of comparing the test statistic to the critical value in hypothesis testing?

  Decide whether to reject H₀
• The mean is calculated by summing all values and dividing by the total number of values
• What does the mode represent in a data set?

  The most frequent value
• Variance is the average squared deviation from the mean.


  True
• Match the measure with its description:

  Mean ↔️ The average value

  Median ↔️ The middle value in order

  Mode ↔️ The most frequent value
• Descriptive statistics are used to summarize sample data, while inferential statistics are used to make inferences about populations.


  True
• Steps to investigate the correlation between temperature and plant growth:

  1️⃣ Collect data on temperature and plant growth

  2️⃣ Calculate the correlation coefficient

  3️⃣ Interpret the results
• What is the typical significance level (α) used in hypothesis testing?

  0.05
• Steps in hypothesis testing:

  1️⃣ State null and alternative hypotheses

  2️⃣ Choose significance level (α)

  3️⃣ Calculate test statistic

  4️⃣ Compare test statistic to critical value
• The median is more robust to outliers
• What is the purpose of measures of dispersion?

  Quantify data spread
• Measures of dispersion provide a comprehensive view of how data is spread around the central values
• What is the formula for variance?

  \frac{\sum (x_{i} - \mu)^{2}}{n - 1}</latex>
• Match the inferential statistical method with its description:

  Hypothesis Testing ↔️ Testing a claim about a population parameter

  Correlation ↔️ Measuring the relationship between two variables

  Regression ↔️ Modeling the relationship between variables
• What is a typical significance level (α) used in hypothesis testing?

  0.05 or 5%
• If the test statistic exceeds the critical value, the null hypothesis is rejected.


  True
• What is the purpose of measures of central tendency?

  Describe typical or central value
• The median is the middle value when the data is arranged in order.


  True
• The range is the difference between the highest and lowest values
• What does standard deviation indicate about a data set?

  Average deviation from the mean
• Inferential statistics are used to make inferences about a population
• What does a correlation coefficient close to 1 indicate?

  Strong positive correlation
• In hypothesis testing, the null hypothesis often states that there is no difference or effect
• If the test statistic exceeds the critical value, the null hypothesis is rejected.


  True
• Match the measure of central tendency with its description:

  Mean ↔️ The average value

  Median ↔️ The middle value in order

  Mode ↔️ The most frequent value
• The mode identifies the most common value in a data set.


  True
• Match the measure of dispersion with its description:

  Range ↔️ Difference between highest and lowest

  Variance ↔️ Average squared deviation from mean

  Standard Deviation ↔️ Square root of variance
• Descriptive statistics include measures of both central tendency and dispersion.


  True
• What is the purpose of descriptive statistics?

  Summarize data
• The median is the middle value when data is arranged in order.


  True
• Match the measure of dispersion with its description:

  Range ↔️ Difference between highest and lowest values

  Variance ↔️ Average squared deviation from the mean

  Standard Deviation ↔️ Square root of variance
• The range is the difference between the highest and lowest values