The average of the weight of the two people who arrived late for this considered case is found being 203 pounds.
How to find the mean of a data set?
Mean(also called average) is the ratio of the sum of the values of the data set to the total number of values available in the data set.
Thus, we get;
[tex]\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}[/tex]
Given that:
- Average of weight of 11 people at party = 128
- New average of total 13 people at party (2 people came late) = 148
Assume that:
- Sum of weight of 11 people who came early = x
- Sum of weight of 2 people who came late = y
Then, we get:
Average of weight of 11 people at party =
[tex]\dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}} = \dfrac{x}{11} =138[/tex]
Thus, we get:
[tex]x = 11 \times 138 = 1,518 \: \rm pounds[/tex]
The weight of all 13 people is sum of weight of 11 people + sum of weight of those 2 people who came late = x + y, therefore, we get:
Average of weight of 13 people at party =
[tex]\dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}} = \dfrac{x+y}{13} = 148[/tex]
Thus, we get:
[tex]\dfrac{1518 + y}{13} = 148\\1518 + y = 13 \times 148\\\\y = 1924 - 1518 = 406 \: \rm pounds[/tex]
That means, sum of weights of 2 people who came late = 406 pounds.
Thus, average weight of the two people who arrived late = [tex]\dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}} = \dfrac{y}{2} = \dfrac{406}{2} = 203 \: \rm pounds[/tex]
Thus, the average of the weight of the two people who arrived late for this considered case is found being 203 pounds.
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