Probability & Statistics

• What are the three main statistics used to analyze data?

  Mean, median, and mode
• What is the mean?

  • The average of a set of numbers
  • Calculated by summing values and dividing by count
• What is the median?

  • The middle value in a sorted data set
  • If even number of values, average the two middle values
• What is the mode?

  • The most frequently occurring value in a data set
  • A data set may have no mode or multiple modes
• If Kayla has 8 numeral cards and removes two, what is the mean of the remaining cards if it is 4?

  The sum of remaining cards is 24
• How do you find the sum of the removed cards if the mean of the remaining cards is known?

  Subtract the sum of remaining cards from total
• What is the formula to calculate the sum of values?

  Sum = Mean × Number of values
• What two cards could Kayla have removed if their sum is 12?

  5 and 7 or 6 and 4
• How do you check if the mean of the remaining cards is correct?

  Add remaining cards and divide by 6
• What are the strengths and weaknesses of the mean, median, and mode?

  Mean:

  • Uses all data
  • Affected by extreme values

  
  

  Median:

  • Not affected by extreme values
  • Value may not exist

  
  

  Mode:

  • Suitable for descriptive data
  • Not always near the middle
• What marks must Joe score in his next test for his new mean and median to be the same?

  Calculate based on current scores
• What is the total frequency of pets owned by students in the class?

  37
• How do you calculate the mean from a frequency table?

  Mean = Total of f × x ÷ Total frequency
• What is the total of f × x for the pets owned frequency table?

  34
• What is the total frequency of students recorded by Maisie?

  150
• How do you estimate the mean time taken by students to travel to school?

  Divide total f × x by total frequency
• Why is the answer to the mean time an estimate?

  Exact data values are unknown
• What is the formula for the range of a data set?

  Range = Largest value - Smallest value
• What is the interquartile range (IQR)?

  IQR = Q₃ - Q₁
• How do you find the lower quartile (Q₁)?

  Identify the 4th value in ordered data
• How do you find the upper quartile (Q₃)?

  Identify the 12th value in ordered data
• What is the golden rule before calculating median or quartiles?

  Arrange data in order of size
• What does a vertical line graph represent?

  Data using straight vertical lines
• What is a time series graph?

  A line graph showing changes over time
• What does correlation in a scatter graph indicate?

  Relationship between two variables
• What is an outlier in data?

  A value that doesn't fit the pattern
• What does correlation not imply?

  That two variables are related
• How do you estimate values using a line of best fit?

  Draw a line close to data points
• What is interpolation in data prediction?

  Predicting within the range of data
• What is extrapolation in data prediction?

  Predicting outside the range of data
• What is the definition of a population in statistics?

  A group from a larger population
• What are the advantages of sampling?

  Cheaper, quicker, and easier to analyze
• What should Ashik do to improve his sample size?

  Survey at least 20 or 30 students
• What is a random sample?

  A sample where everyone has an equal chance
• What is a population in statistics?

  A group of people or items
• Why is sampling used in statistics?

  To make predictions about the whole population
• What are the advantages of sampling?

  • Cheaper than surveying the whole population
  • Quicker data collection
  • Easier data analysis and statistics calculation
• What problem did Ak face with his sample size?

  He selected only 5 students
• How many students should Ashik have surveyed?

  At least 20 or 30 students
• Why is it important to choose a random sample?

  To ensure everyone has an equal chance