Understanding characteristics of normal distribution

• What happens to data points as you move away from the center in a normal distribution?

  Fewer data points are shown
• What is the difference between a symmetric distribution and a skewed distribution?

  • Symmetric distribution: Mean, median, and mode are equal
  • Skewed distribution: Mean, median, and mode are not equal
• What is the mean of the scores 4, 5, 6, 7, 8?

  $6$
• What are the three measures of central tendency?

  Mean, median, and mode
• How is the mean calculated?

  Add all numbers and divide by count
• What percentage of data falls within 3 standard deviations from the mean?

  • 99.7% of data falls within 3 standard deviations
• What is the median of the scores 4, 5, 6, 7, 8?

  $6$
• What shape does a normal distribution create?

  A bell shape
• In a normal distribution, how do the mean, median, and mode relate to each other?

  They are all the same and at the center
• What percentage of data falls within 2 standard deviations from the mean?

  • 95% of data falls within 2 standard deviations
• What is the mode of the scores 4, 5, 6, 6, 7, 8?

  $6$
• What percentage of data is within two standard deviations of the mean?

  95% of data
• What does the shape of the normal distribution curve represent?

  • The distribution of data around the mean
  • The likelihood of data points occurring at different distances from the mean
• What percentage of data is within three standard deviations of the mean?

  99.7% of data
• What does the area under the normal distribution curve represent?

  The total amount of data
• What are the key properties of a normal distribution?

  • Symmetric, bell-shaped curve
  • Mean, median, and mode are all equal
  • 68% of values are within 1 standard deviation of the mean
  • 95% of values are within 2 standard deviations of the mean
  • 99.7% of values are within 3 standard deviations of the mean
• What is the standard deviation represented by the image?

  one standard deviation
• How do you find the median if there is an even number of data points?

  Average the two middle numbers
• How does the normal distribution curve relate to the percentage of data within different standard deviations of the mean?

  The curve shows that as you move further from the mean, the percentage of data decreases exponentially
• What is the median in a data set?

  The middle number when data is ordered
• What percentage of data is within one standard deviation of the mean?

  68% of data
• If a data point is 2 standard deviations away from the mean, what percentage of the data is further from the mean than that point?

  5%
• How does the standard deviation help in data analysis?

  It indicates how typical or extreme a data point is
• What does the standard deviation measure?

  Data spread from the mean
• What shape does a normal distribution resemble?

  A symmetrical bell shape
• How can a normal distribution be illustrated using student grades?

  • Most students receive average marks
  • Fewer students achieve very high grades
  • Fewer students receive very low grades
• What is the mode in a data set?

  The number that appears most often
• Where is the center of a normal distribution located?

  Where most data points are clustered
• What is the mean value of the distribution shown in the image?

  1211
• What do percentiles indicate about a data point?

  They show the percentage of data below it
• How does a skewed distribution differ from a normal distribution?

  A skewed distribution loses its symmetric appearance
• How do the positions of the mean, median, and mode differ between the symmetric and skewed distributions?

  • Symmetric: Mean = Median = Mode
  • Skewed: Mean ≠ Median ≠ Mode
• What are the key statistical measures shown in the two distribution graphs?

  • Mean
  • Median
  • Mode
• What type of distribution is shown in the image?

  Normal
• What is the relationship between the mean, median, and mode in a skewed distribution?

  They are not all equal
• What is the relationship between the mean, median, and mode in a symmetric distribution?

  They are all equal
• How does the shape of the symmetric distribution curve differ from the skewed distribution curve?

  The symmetric distribution is bell-shaped, while the skewed distribution is asymmetric with one tail longer
• What happens to the measures of central tendency when data is skewed?

  They separate and lose symmetry
• How do the shapes of the symmetric and skewed distributions differ?

  • Symmetric distribution: Bell-shaped curve
  • Skewed distribution: Asymmetric, with one tail longer than the other
• What does symmetry in a normal distribution indicate?

  It indicates equal distribution around the center