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IB DP Maths: AA SL復習筆記4.1.3 Frequency Tables

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月18日 下午12:43

Ungrouped Data

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?xi?by its frequency?fi
    • Summing to get Σfixi
    • Dividing by the total frequency?n?=?Σfi
    • 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
    • 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

Exam Tip

  • Always check whether your answers make sense when using your GDC
    • The value for a measure of central tendency should be within the range of data

Worked Example

The frequency table below gives information number of pets owned by 30 students in a class.

 

Number of pets 0 1 2 3
Frequency 11 5 8 6

 

Find

a)? ? ? ? the mode.

4-1-3-ib-ai-aa-sl-ungrouped-data-a-we-solution

b)? ? ? ?the median.

4-1-3-ib-ai-aa-sl-ungrouped-data-b-we-solution

c)? ? ? ? the mean.

4-1-3-ib-ai-aa-sl-ungrouped-data-c-we-solution

d)? ? ? ? the standard deviation.

4-1-3-ib-ai-aa-sl-ungrouped-data-d-we-solution

Grouped Data

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
      • 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)?xi?for each class
    • Multiplying each value by the class frequency?fi
    • Summing to get Σfixi
    • Dividing by the total frequency?n?=?Σfi
    • 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
  • 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

Exam Tip

Worked Example

a)? ? ? ? Write down the modal class.

4-1-3-ib-ai-aa-sl-grouped-data-a-we-solution

b)? ? ? ?Write down the mid-interval value of the modal class.

4-1-3-ib-ai-aa-sl-grouped-data-b-we-solution

c)? ? ? ? Calculate an estimate for the mean height.

4-1-3-ib-ai-aa-sl-grouped-data-c-we-solution

 

 

 

 

 

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