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IB DP Maths: AI 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19日下午2:44

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

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

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

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

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

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

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

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