frequency table and graph are summaries of the results of an activity. You can use these tables or graphs to discover or estimate the:
  • mode;
  • median;
  • mean;
  • quartiles; and
  • inter-quartile range.
These are the results from 20 rolls of a die. Fill in the key summary statistics for this data once you have made the calculation
Die resultFrequency
11
25
34
44
53
63

Total = 20
Mode = ?
Mean = ?
Lower quartile = ?
Median = ?
Upper quartile = ?
Interquartile range = ?
Possible answers
Which score occurs most often? The mode = 2.
Add up all the values and divide by 20 (the number of rolls of the die). Mean = 3.6.
Which score has 25% of the results below it? Lower quartile = 2.
Which score is the middle value? For 20 scores the middle value is between the tenth and eleventh score in order from the lowest to highest. Median = 3.5.
Which score has 75% of the results below it? Upper quartile = 5.
What is the difference between the upper and lower quartiles? Interquartile range = 3.

Mean from frequency tables - discrete data
Heather asks her friends to tell her the size of their families. She records the data in a frequency table.
Family sizeFrequencyNumber of people
100
224
3515
4832
5420
600
717

2078
To calculate the mean number of people in each family we need to find the total number of people in the survey and the number of families.
In this survey a total of 20 families were surveyed and it was found that there were 78 people altogether.
Therefore the mean = 78/20 = 3.9 people per family.
Finding the mean from a discrete frequency table
  • The frequency table tells you how many there are for each value.
  • So you can work out the sub-total value of the results in each column by multiplying: value x frequency.
  • Then you can add them all to find the grand total of these sub-totals.
  • The mean is just the average. So you divide the grand total by the total frequency: total value divided by total frequency = mean.

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