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 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
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.
b)the median.
c)the mean.
d)the standard deviation.
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
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 exactmean 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
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 xi 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
Exam Tip
Worked Exampleb)Write down the mid-interval value of the modal class.