Final answer:
To find the variance of the data, calculate the mean of the hand lengths and then use the formula to find the sum of squares of differences. Divide it by the total number of data to get the variance.
Step-by-step explanation:
To find the variance of the data, you can use the formula:
Variance = Sum of Squares of Differences / Total Number of Data
First, calculate the mean of the data by summing up all the hand lengths and dividing by the total number of members in the orchestra:
Mean = (50 * 51) / 2 = 1275
Next, calculate the sum of squares of differences by subtracting the mean from each hand length, squaring the result, and summing them:
Sum of Squares of Differences = (50 * (50 - 1275)^2 + 51 * (51 - 1275)^2) = 161250
Finally, divide the sum of squares of differences by the total number of data:
Variance = 161250 / 101 = 1599.50495
Therefore, the variance of the data is approximately 1599.50495