7.5.1.4 Distributions

• What does a distribution in statistics refer to?

  Spread of a data set
• In a normal distribution, the mean, median, and mode are equal.
• A positively skewed distribution has a tail to the right
• What is a bimodal distribution characterized by?

  Two distinct peaks
• Order the steps to represent distributions using histograms and frequency tables.

  1️⃣ Collect data

  2️⃣ Create a frequency table

  3️⃣ Draw a histogram
• What is the formula for calculating the mean in statistics?

  $\text{Mean} =$$\frac{\sum_{i = 1}^{n} x_{i}}{n}$
• The mode is the most frequently occurring value
• What type of distribution is symmetrical and bell-shaped with the mean, median, and mode equal?

  Normal distribution
• Match the distribution type with its mean, median, and mode relationship:

  Normal ↔️ Mean = Median = Mode

  Positively Skewed ↔️ Mean > Median > Mode

  Negatively Skewed ↔️ Mean < Median < Mode
• A bimodal distribution has two distinct peaks.
• What are the two parameters that characterize a normal distribution?

  Mean and standard deviation
• In a uniform distribution, all values are equally likely
• Which two methods are used to represent distributions?

  Histograms and frequency tables
• The mean is the average of all values in a data set.
• The median is the middle value when data is sorted.
• What is the formula for the standard deviation in a normal distribution?

  $\sigma =$$\sqrt{\frac{\sum_{i = 1}^{n} (x_{i} - \mu)^{2}}{n - 1}}$
• Match the distribution type with its shape:

  Normal ↔️ Bell-shaped

  Skewed ↔️ Asymmetrical with tail

  Bimodal ↔️ Two distinct peaks
• What is the shape of a positively skewed distribution?

  Asymmetrical with a tail
• In a uniform distribution, the mean, median, and mode are approximately equal.
• A bimodal distribution has two distinct peaks
• How is the mean calculated in a distribution?

  \frac{\sum_{i = 1}^{n} x_{i}}{n}</latex>
• The median is the middle value when data is sorted.
• The mode is the most frequently occurring value
• For what type of distribution is the mean most useful as a measure of central tendency?

  Normal distributions
• The median is more useful than the mean for skewed distributions.
• The mode is particularly useful for bimodal or categorical data
• Match the measure of central tendency with its definition:

  Mean ↔️ Average of all values

  Median ↔️ Middle value when sorted

  Mode ↔️ Most frequent value
• What does the range measure in a distribution?

  The spread of data
• The standard deviation is the square root of the variance.
• The range is sensitive to outliers
• Why is the variance difficult to interpret directly?

  Units are squared
• The standard deviation measures typical deviation from the mean.
• What is the standard deviation formula based on the variance?

  $\sqrt{\text{Variance}}$
• The range is the difference between the maximum and minimum values
• The range is highly sensitive to outliers.
• What does the variance measure?

  Total spread of data
• The units of variance are easy to interpret directly.

  False
• The standard deviation is the square root of the variance
• The standard deviation is affected by outliers.
• What does a distribution in statistics describe?

  Spread or pattern of data