Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers
To find the mean, add the values and divide by how many there are, as you did with five pumpkins. One mean can hide differences between two data sets. The median is the middle value after ordering, or the mean of the two middle values when the count is even. The mode is the value that appears most often. The range measures spread: largest value minus smallest.
A team's ages are 12, 14, 12, 15, 12. Line them up in order: 12, 12, 12, 14, 15. The middle number is 12, so the median is 12. Since 12 shows up three times, more than any other age, the mode is also 12.
Outliers are values far from the rest. They can pull the mean up or down. The median uses the middle positions and is usually less affected by an extreme value. Adding or removing values can still change the median. When a data set has an outlier, the median often gives a better picture of a typical value.
Two pumpkin beds are weighed. Gate bed gives 3, 5, 6, 6 and 30 kg. Shed bed gives 8, 9, 9, 11 and 13 kg. Both add up to 50 kg, so both means are 10 kg. Put each set in order: Gate bed's median is 6 kg and Shed bed's is 9 kg. Their ranges also differ: 27 kg for Gate bed and 5 kg for Shed bed. To compare two sets, work out the same measure for both and say which measure you used.
Median uses the middle value or pair; mode is most common; range is biggest minus smallest. Outliers can pull the mean up or down. Compare the same measures across sets.
Practice questions and "One big pocket" were written for this dataset. The rewritten reading was written for this dataset. Adapted reading summaries: Khan Academy, "Center, spread, and shape of distributions"; OER Commons lesson record, "Understanding Mean, Median, and Mode". Source licenses are not specified.
Last autumn you and Mia chalked one number on the pumpkin poster: the mean, one fair number for a whole bed. This year the allotment has two pumpkin beds, and Leo wants to know which one did better.
Gate bed grew five pumpkins: 3, 5, 6, 6 and 30 kg. What is Gate bed's mean mass?
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