CHAPTER 3

• What is a measure of central tendency?

  It represents the 'centre' of data.
• What are the three types of averages?

  Mode, median, and mean.
• What does the mode represent in a data set?

  The most common value in the data set.
• What is a modal class?

  The class with the highest frequency.
• How is the median defined?

  The middle value of a data set.
• What are the steps to find the median of discrete data?

  1. Order numbers from smallest to largest.
  2. Calculate median position: $\frac{1}{2}(n + 1)$.
  3. Find the median value from the ordered list.
  4. If position is decimal, average the two surrounding values.
• How do you find the median position in a list of values?

  Calculate $\frac{1}{2}(n + 1)$.
• If the total frequency is 23, what is the median position?

  12th number in the ordered list.
• What should you do if the median position is a decimal value?

  Average the two surrounding values.
• How do you find the median in a frequency table?

  Add frequencies until reaching the median position.
• What is the process for finding the median of grouped data?

  1. Calculate $\frac{1}{2}n$ for median position.
  2. Identify the median class from cumulative frequency.
  3. Estimate median using linear interpolation.
• What is the formula for estimating the median using linear interpolation?

  Add the lower bound to the calculated value.
• What is the mean also known as?

  Arithmetic mean.
• What are the steps to calculate the mean for discrete data?

  1. Add all the values.
  2. Divide by the number of values.
• What is the formula for the mean?

  $\bar{x} =$$\frac{\sum x}{n}$
• What does $\sum$ represent in the mean formula?


  Sum of all values.
• How do you calculate the mean from a frequency table (not grouped)?

  1. Add a column for $f \times x$.
  2. Multiply values in the first two columns.
  3. Sum the $f \times x$ column.
  4. Sum the frequency column.
  5. Divide total $f \times x$ by total frequency.
• What are the steps to calculate the mean from a grouped frequency table?

  1. Add columns for midpoint and $f \times midpoint$.
  2. Calculate midpoints of class intervals.
  3. Multiply midpoints by frequencies.
  4. Sum $f \times midpoint$ column.
  5. Sum frequency column.
  6. Divide total $f \times midpoint$ by total frequency.
• What is a weighted mean used for?

  Combining data with different importance levels.
• What is the formula for the weighted mean?

  $Weighted Mean =$$\frac{\sum(weight \times value)}{\sum(weights)}$
• What is the geometric mean useful for?

  Comparing growth rates across different values.
• What is the formula for the geometric mean?

  $Geometric Mean =$$\sqrt[n]{value_1 \times value_2 \times \ldots \times value_n}$
• What is the process for transforming data to make calculations easier?

  1. Subtract a number from all values.
  2. Multiply/divide by a number.
  3. Find the mean of new numbers.
  4. Reverse the transformation.
• How does adding a value greater than the median affect the median?

  The median might increase.
• What happens to the median if a value smaller than it is added?

  The median might decrease.
• How does removing a value greater than the median affect it?

  The median might decrease.
• What happens if you remove a value smaller than the median?

  The median might increase.
• What is the effect on the median if one value greater and one smaller than it are added or removed?

  The median stays the same.
• How does adding a value greater than the mean affect the mean?

  The mean increases.
• What happens if you remove a value less than the mean?

  The mean increases.
• How does adding a value less than the mean affect it?

  The mean decreases.
• What happens if you remove a value greater than the mean?

  The mean decreases.
• How does replacing a value with a greater or smaller number affect the mean?

  The mean will change.
• What are the advantages and disadvantages of using mode, median, and mean?

  Advantages:

  • Mode: Easy to use, unaffected by extremes.
  • Median: Unaffected by outliers, best for skewed data.
  • Mean: Uses all data, useful for calculations.

  
  

  Disadvantages:

  • Mode: May not exist or be misleading.
  • Median: May not be representative.
  • Mean: Affected by extremes, not always a data value.
• What does the range measure in data?

  How spread out the data is.
• How is the range calculated?

  Largest value minus smallest value.
• What is the interquartile range (IQR)?

  The middle 50% of the ordered data.
• How is the IQR calculated?

  Upper quartile minus lower quartile.
• What is the lower quartile (LQ)?

  Value ¼ of the way through the data.
• What is the upper quartile (UQ)?

  Value ¾ of the way through the data.