Final answer:
To find the range, subtract the minimum value from the maximum value. To find the standard deviation, calculate the mean, then calculate the squared difference between each data point and the mean, sum up these squared differences, divide by the number of data points, and take the square root of the result.
Step-by-step explanation:
To find the range, we need to subtract the minimum value from the maximum value in the data set. In this case, we have a sample of 24 children and we need to find the range of the number of hours spent watching TV last week. Let's say the minimum number of hours is 10 and the maximum number of hours is 20. The range would be 20 - 10 = 10.
To find the standard deviation, we need to calculate the average or mean of the data set. Let's say the mean is 15. Then, we need to calculate the squared difference between each data point and the mean, sum up these squared differences, divide by the number of data points, and take the square root of the result. This will give us the standard deviation.
For example, if the data set is {10, 12, 15, 18, 20}, the mean is (10 + 12 + 15 + 18 + 20) / 5 = 15. Then, the squared differences are (10 - 15)^2, (12 - 15)^2, (15 - 15)^2, (18 - 15)^2, and (20 - 15)^2. Summing up these squared differences gives us 10 + 9 + 0 + 9 + 25 = 53. Dividing by the number of data points, which is 5, gives us 53 / 5 = 10.6. Taking the square root of 10.6 gives us the standard deviation, which is approximately 3.26.