Final answer:
To determine the mean of the sample, we deduced the number of values in the sample by understanding the contribution of the +2 in the sum to the overall increase. We found there are 10 values, and by dividing the sum of 'x' (which is 10) by the number of values, we determined the mean to be 1.
Step-by-step explanation:
To find the mean of the given sample, we first need to understand what the given symbols represent. The symbol Σ (sigma) represents the sum of all values in a set. The expressions Σ(x+2)=30 and Σx=10 suggest that if you sum all the 'x' values and then add 2 to each before summing, you will get 30, whereas if you just sum the 'x' values, you get 10.
To find the mean (average), we would typically divide the sum of all the 'x' values by the number of values in the sample. However, we are not given the number of values directly, but we can deduce it. If adding 2 to each value in the sum leads to an increase from 10 to 30, and this increase is entirely due to adding 2 for each value, we can infer that there must be Σ20 = 20, hence getting a total increase of 20 when adding 2 for each value.
Now that we know there are 10 values, we can calculate the mean by dividing the sum of 'x' values by the number of values:
Mean = Σx / n = 10 / 10 = 1
The mean of the sample is therefore 1.