Calculate the mean and median of both raw and grouped data, and understand when each measure is most useful.
The mean (average) is found by summing all values and dividing by the count. For grouped data, each value is weighted by its frequency.
Find the mean of: 12, 18, 20, 25, 15.
(12+18+20+25+15)/5=90/5=18
Find the mean of data with values 5(freq 2), 8(freq 3), 10(freq 5).
(5×2+8×3+10×5)/(2+3+5)=(10+24+50)/10=84/10=8.4
The median is the middle value when data is arranged in order. For an even number of values, it's the average of the two middle values.
Find the median of: 4, 9, 2, 7, 5 (arrange first).
Arranged: 2,4,5,7,9; median=5 (middle value)
Find the median of: 3, 8, 6, 12 (arrange first).
Arranged: 3,6,8,12; median=(6+8)/2=7
1. Find the mean of: 22, 28, 30, 35, 20.
2. Find the mean of data with values 3(freq 4), 6(freq 6).
3. Find the median of: 15, 9, 22, 6, 18 (arrange first).
4. Find the median of: 4, 10, 8, 14 (arrange first).
5. For a data set with an odd number of values, is the median always one of the original values?