In a study about children’s pocket money, two samples of schoolchildren were asked how much money they received each week. In one sample, of size 25, the mean is £6.00. In the other sample, of size 43, the mean is £9.21.
Calculate the mean based on the combined sample. Give your answer correct to two decimal places.
(25 * 6) + (43 * 9.21) = 150 + 396.03 = 546.03
546.03 / 68 = ?
8.03 (to 2 d.p) Thanks
You're welcome, Jay.
To calculate the mean based on the combined sample, you need to take into account the sample sizes and means of both samples. The formula to find the mean based on the combined sample is:
Mean(combined sample) = (n1 * mean1 + n2 * mean2) / (n1 + n2)
where n1 is the sample size of the first sample, mean1 is the mean of the first sample, n2 is the sample size of the second sample, and mean2 is the mean of the second sample.
In this case, n1 = 25, mean1 = £6.00, n2 = 43, and mean2 = £9.21.
Plugging in these values into the formula, we get:
Mean(combined sample) = (25 * £6.00 + 43 * £9.21) / (25 + 43)
First, let's calculate the numerator:
Numerator = (25 * £6.00 + 43 * £9.21) = £150.00 + £396.03 = £546.03
Now let's calculate the denominator:
Denominator = (25 + 43) = 68
Finally, divide the numerator by the denominator to find the mean based on the combined sample:
Mean(combined sample) = £546.03 / 68 = £8.03
Therefore, the mean based on the combined sample is £8.03.