Summarize Numerical Data
Mean, median, and mode are three kind presentation of the “centre”.
Mean: is the “average” you’re used to, where you add up all the numbers and then divide by the number of numbers.
Median is the “middle” value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first.
Mode is the value that occurs most often. If no number is repeated, then there is no mode for the list.
Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
Mean: (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
Median: 13, 13, 13, 13, 14, 14, 16, 18, 21
Mode: the occur of 13 is more than other numbers. So 13 is the mode.
- mean: 15
- median: 14
- mode: 13
Interquartile range (IQR), Range and Standard Deviation are two summarise of data spread.
Interquartile range (IQR)
The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles.
IQR also relies on Q1, Q2, and Q3, respectively.
- Q1 is the “middle” value in the first half of the rank-ordered data set.
- Q2 is the median value in the set.
- Q3 is the “middle” value in the second half of the rank-ordered data set.
Range is the difference between the largest value and smallest value.
The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)
The formula is easy: it is the square root of the Variance.
Sample Standard Deviation:
The Variance is defined as: the average of the squared differences from the Mean.
5, 8, 4, 4, 6, 3, 8
Put them in order: 3, 4, 4, 5, 6, 8, 8
Cut the list into quarters:
- Quartile 1 (Q1) = 4
- Quartile 2 (Q2), which is also the Median, = 5
- Quartile 3 (Q3) = 8
- IQR= Q3-Q1= 8-4 =4
- Range = 8 -3 = 5
- Standard Deviation =1.988