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 booklet

• • Your?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

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
  • Class intervals will be written using inequalities and without gaps

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