4.4.4 Comparing Distributions
Comparing distributions is a statistical analysis technique used to determine whether two or more sets of data come from the same or different populations.
A distribution refers to the way in which the data is spread out or distributed in a dataset.
Comparing distributions involves examining the shape, center, and spread of the data in each dataset, and identifying any differences or similarities between them.
To compare averages of two datasets
Choose the appropriate average (mean, mode, median)
Mean includes all the data
Mode can be used for non-numerical data
Median is not affected by extreme values
Consider whether a larger or smaller average is preferable.
When comparing puzzle completion times, the smaller the average, the better.
When comparing test scores, the higher the average, the better.
Give numerical values for the average and compare them explicitly.
The average weight of a dog is \( 17 \)kg, which is higher than the average weight of a cat, which is \( 13 \)kg.
Then provide your context comparison.
Cats have a smaller interquartile range, implying that their weights are more consistent and less spread out than dogs’.
Test yourself
Question 1:
Roberto records the value of each of the coins he has at home.
The table shows the results.
Find the range.
[1]
Find the mode.
[1]
Find the median.
[1]
Work out the total value of Roberto’s coins.
[1]
Work out the mean.
[1]
Question 2:
The table gives information about the length of time, in minutes that each of \( 60 \) students took to
travel to school on Monday.
Write down the modal class interval.
[1]
Question 3:
The heights, \( h \), meters, of the \( 120 \) boys in an athletics club are recorded.
The table shows information about the heights of the boys.
Calculate an estimate of the mean height.
[4]
Question 4:
The table shows the marks scored by some students in a test.
Calculate the mean mark.
[3]
Question 5:
\( 200 \) students estimate the total area, \( A \) m2, of the windows in the classroom.
The table shows the results.
Calculate an estimate of the mean.
You must show all your working.
[4]
Question 6:
The frequency table shows information about the number of books read by some students in a
reading marathon.
The mean number of books read is \( 4.28 \).
Find the value of \( x \).
[3]
Write down the mode.
[1]
Write down the median.
[1]