IB DP Maths: AI HL复习笔记4.1.4 Frequency Tables

How are frequency tables used for ungrouped data?

• Frequency tables can be used for ungrouped data when you have lots of the same values within a data set
  • They can be used to collect and present data easily
• If the value 4 has a frequency of 3 this means that there are three 4’s in the data set

How are measures of central tendency calculated from frequency tables with ungrouped data?

• The mode is the value that has the highest frequency
• The median is the middle value
  • Use cumulative frequencies (running totals) to find the median
• The mean can be calculated by
  • Multiplying each value x_i by its frequency f_i
  • Summing to get Σf_ix_i
  • Dividing by the total frequency n = Σf_i
  • This is given in the formula bookletYour GDC can calculate these statistical measures if you input the values and their frequencies using the statistics mode
  • How are measures of dispersion calculated from frequency tables with ungrouped data?

• The range is the largest value of the data minus the smallest value of the data
• The interquartile range is calculated by

• • The quartiles can be found by using your GDC and inputting the values and their frequencies
• The standard deviation and variance can be calculated by hand using the formulae

• • You do not need to learn these formulae as you will be expected to use your GDC to find the standard deviation and variance
    • You may want to see these formulae to deepen your understanding

How are frequency tables used for grouped data?

• Frequency tables can be used for grouped data when you have lots of the same values within the same interval
  • • You do not know the exact data values when you are given grouped data

How are measures of central tendency calculated from frequency tables with grouped data?

• The modal class is the class that has the highest frequency
  • This is for equal class intervals only
• The median is the middle value
  • The exact value can not be calculated but it can be estimated by using a cumulative frequency graph
• The exact mean can not be calculated as you do not have the raw data
• The mean can be estimated by
  • Identifying the mid-interval value (midpoint) x_i for each class
  • Multiplying each value by the class frequency f_i
  • Summing to get Σf_ix_i
  • Dividing by the total frequency n = Σf_i
  • This is given in the formula booklet

• • Your GDC can estimate the mean if you input the mid-interval values and the class frequencies using the statistics mode

How are measures of dispersion calculated from frequency tables with grouped data?

• The exact range can not be calculated as the largest and smallest values are unknown
• The interquartile range can be estimated by

• • Estimates of the quartiles can be found by using a cumulative frequency graph
• The standard deviation and variance can be estimated using the mid-interval values x_i in the formulae
  • You do not need to learn these formulae as you will be expected to use your GDC to estimate the standard deviation and variance using the mid-interval values

• • • You may want to see these formulae to deepen your understanding