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What are measures of central tendency?
What are measures of central tendency?
Mean
Mean
The mean is the statistical calculation which is the arithmetic average.
Median
Median
The median is the middle value of an ordered data set.
The median splits the data in half, so for an odd number of data values the median will be one of the original values, however for an even amount number of data values the median is the average of the two middle ones.
If there are n values in the data set, the median is the one (n+1)/2 th position in the data.
Mode
Mode
For discrete data, the mode is the most frequently occurring value in the data set.
For continuous data, no two values will be exactly the same so instead we talk about a modal class.
If a data set has two modes it is called bimodal.
For a review on Mean, Median and Mode watch the video below. Then try and answer the practice questions by clicking on the link below.
For a review on Mean, Median and Mode watch the video below. Then try and answer the practice questions by clicking on the link below.
If you are confident with averages you may want to try these 'wordy' questions as a challenge.
If you are confident with averages you may want to try these 'wordy' questions as a challenge.
Investigation: The effects of outliers and extreme values.
Investigation: The effects of outliers and extreme values.
Consider the data set 4, 5, 6, 6, 6, 7, 7, 8, 9, 10. Calculate:
(a) Mean (b) Median (c) Mode
Suppose we introduce an extreme value of 100 to the data set, so that now it is 4, 5, 6, 6, 6, 7, 7, 8, 9, 10, 100. Now calculate:
(a) Mean (b) Median (c) Mode
Comment on the effect that the outlier has on each of the three measures of central tendency.
Which of the 3 measures is most effected by outliers?
When is it not appropriate to use certain measures?
Choosing the appropriate measure
Choosing the appropriate measure
The mean, median and mode can be used to determine the centre of a data set. The most appropriate is determined by the type of data that is being considered.
It may be appropriate to use the mode when considering shoe sizes. When considering the average price of computers, the mean is the most appropriate. However when considering average house prices, as the mean is skewed by extreme high values and low values, the median will be the best average.
Therefore, when considering the most appropriate measure, you have to consider the real world scenario.
Technology
Technology
Watch the video to see how you can use your calculators to find the mean of different data sets. Follow along and practice this skill to make sure you are happy with it.
As all of our data is on google sheets, we can use the functions within google sheets to easily calculate the mean, median and mode for large data sources.
This is really helpful and useful to us as we 200 countries and 12 different years to compare!
Frequency Tables
Frequency Tables
Answers
Answers
Mean = 3.25 aces
Median = 28th value = 3 aces
Mode = 3 aces
Extension: How can we find averages from grouped frequency tables?
Extension: How can we find averages from grouped frequency tables?
Interdisciplinary Component
Interdisciplinary Component
Select your chosen sport from the data, or sports that you think are relevant. To explore which components of fitness are relevant calculate the mean, median and mode. Determine which one is most effective in this situation and what you can infer about the data.
You can use technology to assist you.
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