Answer
The mean, median, trimmed mean and the weighted mean can be calculated for quantitative data only, while the mode can be calculated for both quantitative and qualitative data.
Work Step by Step
The following data give the money spent (in dollars) on computer game during 2019 by 10 adolescents in from a college.
560, 380, 320, 250, 55, 85, 125, 150 175, 200
∑x = 55+85+125+150+175+200+250+320+380+560 = 2300
x ̅=(∑x)/n=2300/10=230 dollars
These 10 adolescents spent an average of 230 dollars on computer game during 2019.
To find the median, we rank the given data in increasing order as follows:
55,85,125,150,175,200,250,320,380, 560
The median will be given by the average of the fifth and the sixth values as follows:
Median = Average of the two middle values = $(175+200)/2 = 97.5 $dollars.
To calculate the 10% trimmed mean, it means
10% of 10 values = 10(0.10) = 1
Hence one value from each end of the ranked data are dropped and the data set is left with the following eight values:
85,125,150, 175, 200, 250, 320, 380.
∑x = 85+125+150+175+200+250+320+380= 1685
10% Trimmed Mean = 1685/8 = 210.625 = 210.63 dollars
There is no mode for this data set.
On the other hand, the mode can be used to calculate for qualitative data, for example the tourists that visited the zoo for a day are American, Chinese and Korean. Suppose that there are the most number of Chinese tourists visiting the zoo that day, hence they are \the mode for this data set.
To illustrate an example for calculating the weighted mean, Isaac bought gas for her car four times during May 2019. She bought 8 gallons at a price of $2.65, 10 gallons at a price of $2.70, 9 gallons at a price of $3.00 and 13 gallons at a price of $2.85.
x denote the variable of the price of the gas, while w denotes the weighted mean. To find the weighted mean, we use the formula = ∑xw \div∑w.
As illustrated in the examples above, we can conclude that the mean, the median, the trimmed mean and the weighted mean can be calculated for quantitative data only, while the mode can be calculated for both quantitative and qualitative data.
