Investigating Variation

• What is the focus of the section titled "Investigating Variation"?

  How variation is studied and analyzed
• Why is it important to know the causes of variation in a population?

  To determine if it's due to genetics or environment
• What is variation?

  Differences that exist between individuals
• What causes variation between species?

  Different genes in different species
• What causes variation within a species?

  Different alleles of the same genes
• How can environmental factors cause variation within a species?

  Through differences in climate, food, and lifestyle
• What is the primary cause of most variation within a species?

  A combination of genetic and environmental factors
• Why do researchers use population samples instead of studying the whole population?

  It's often too time-consuming or impossible
• What is the purpose of random sampling in studying variation?

  To ensure the sample accurately represents the population
• How can you select random sample sites in a field?

  By using a grid and random number generator
• Why is statistical analysis important in studying variation?

  To confirm results reflect the whole population
• What does the mean represent in a sample?

  The average of the values collected
• How do you calculate the mean?

  Sum of values divided by number of values
• What does a variation in mean height indicate?

  Differences in growth conditions or genetics
• What is a normal distribution?

  A symmetrical distribution around the mean
• What does the standard deviation measure?

  The spread of values around the mean
• How does the shape of a normal distribution graph change with standard deviation?

  Flatter with large standard deviation, steeper with small
• What does a small standard deviation indicate about data variation?

  Values are similar and close to the mean
• What does a large standard deviation indicate about data variation?

  Values vary a lot from the mean
• How do the heights of trees in woodland A and B compare?

  Woodland B has taller trees with more variation
• What is the formula for finding the standard deviation of a group of values?

  $S =$$\sqrt{\frac{\Sigma (x - \bar{x})^2}{n - 1}}$
• What does the symbol 'x' represent in the standard deviation formula?

  'x' represents a value in the dataset
• What does the term '(x - x)'² mean in the context of standard deviation?

  It means to take the value away from the mean
• What does 'n' stand for in the standard deviation formula?


  'n' stands for the number of values
• What is the process to calculate standard deviation?

  1. Write out the equation: $S =$$\sqrt{\frac{\Sigma (x - \bar{x})^2}{n - 1}}$
  2. Calculate the mean of the dataset.
  3. Subtract the mean from each value and square the result.
  4. Sum all squared results.
  5. Divide by the number of values minus one.
  6. Take the square root of the result.
• If the heights of trees are 22, 27, 26, and 29, what is the mean height?

  26
• How do you calculate '(x - x)'² for the height of 22 in the dataset?

  (22 - 26)² = 16
• What is the squared difference for the height of 27?

  (27 - 26)² = 1
• What is the squared difference for the height of 26?

  (26 - 26)² = 0
• What is the squared difference for the height of 29?

  (29 - 26)² = 9
• How do you find the total of squared differences for the heights of the trees?

  Sum the squared differences: 16 + 1 + 0 + 9 = 26
• What is the final step to calculate the standard deviation after summing squared differences?

  Divide by the number of values minus one
• What is the square root of 26 in the context of standard deviation?

  Approximately 5.1
• What are the two methods of calculating dispersion of data?

  1. Standard deviation
  2. Range
• What is standard deviation used for?

  Calculating the dispersion of data
• What is another method of calculating dispersion mentioned?

  By looking at the range
• Where can you find more information about the range method?

  See page 5
• What is the result of the square root of $8.66$?


  $2.9$
• What is standard deviation used for?

  • Calculating the dispersion of data
  • Measures how spread out the values are
• How is standard deviation calculated using the range method?

  By looking at the highest and lowest figures