Mean:
The mean, also known as the average, is a measure of central tendency that represents the sum of all the values in a dataset divided by the total number of values. To calculate the mean for the given data:

Step 1: Multiply each value by its corresponding frequency.
0*3 + 10*6 + 20*13 + 30*15 + 40*10 + 50*4 + 60*9 = 0 + 60 + 260 + 450 + 400 + 200 + 540 = 1910

Step 2: Sum up the products of values and frequencies.
3 + 6 + 13 + 15 + 10 + 4 + 9 = 60

Step 3: Divide the sum from step 1 by the sum from step 2.
Mean = 1910 / 60 = 31.83

Therefore, the mean of the given data is approximately 31.83.

Variance:
Variance is a measure of dispersion that quantifies the spread or variability of the data points in a dataset. It is calculated by finding the average of the squared differences between each data point and the mean. To calculate the variance for the given data:

Step 1: Calculate the squared differences between each value and the mean.
(0 - 31.83)^2 * 3 + (10 - 31.83)^2 * 6 + (20 - 31.83)^2 * 13 + (30 - 31.83)^2 * 15 + (40 - 31.83)^2 * 10 + (50 - 31.83)^2 * 4 + (60 - 31.83)^2 * 9 = 18740.15

Step 2: Multiply each squared difference by its corresponding frequency.
18740.15

Step 3: Sum up the products from step 2.
Variance = 18740.15 / 60 = 312.34

Therefore, the variance of the given data is approximately 312.34.

Standard Deviation:
The standard deviation is a measure of dispersion that quantifies the average distance between each data point and the mean. It is the square root of the variance. To calculate the standard deviation for the given data:

Standard Deviation = sqrt(Variance) = sqrt(312.34) = 17.66

Therefore, the standard deviation of the given data is approximately 17.66.

Confidence Interval:
A confidence interval is a range of values within which we can be confident (with a certain level of confidence) that the true population mean lies. To calculate the confidence interval for the given data, we need to know the sample size and the desired level of confidence.

Let's assume a sample size of 60 (since the sum of frequencies is 60) and a desired level of confidence of 95% (which corresponds to a z-score of 1.96).

Step 1: Calculate the standard error of the mean.
Standard Error = Standard Deviation / sqrt(sample size) = 17.66 / sqrt(60) = 2.28

Step 2: Calculate the margin of error.
Margin of Error = z-score * Standard Error = 1.96 * 2.28 = 4.47

Step