With this information, calculate the mean and standard deviation of hours spent watching television by the 220 students.
The formula for the arithmetic mean of a frequency distribution is the sum of the product of the midpoint and the frequency for each data range divided by the sample size.
Taking the square root of the variance gives us the units used in the original scale and this is the standard deviation.
When analysing normally distributed data, standard deviation can be used in conjunction with the mean in order to calculate data intervals.This makes standard deviation a very useful measure of spread for symmetrical distributions with no outliers.Multiply the frequency of each class by the class midpoint.For example, a stock price table could consist of the following price ranges in the data class column - 10 to 12, 13 to 15 and 16 to 18 - and 10, 20 and 30 for the corresponding frequencies.The mean (mu) is the sum of divided by, which is the sum of frequencies.6,560 (2 X 12 code 93 barcode maker 12 X 17 23 X 22 60 X 27 77 X 32 38 X 37 8 X 42) Then, calculate the numbers for the xf, (x - ), (x - )2 and (x - )2f formulas.Continuing with the example, the mean is equal to the sum of the following midpoint and frequency multiplications - 11 multiplied by 10, 14 multiplied by 20 and 17 multiplied by 30 - divided.First, calculate the mean: Now, find the standard deviation.Although standard deviation is less susceptible to extreme values than the range, standard deviation is still more sensitive than the semi-quartile range.For example, a measure of two large companies with a difference of 10,000 in annual revenues is considered pretty close, while the measure of two individuals with a weight difference of 30 kilograms is considered far apart.Each egg was weighed and recorded as follows: 60 g, 56 g, 61 g, 68 g, 51 g, 53 g, 69 g,.Use a software spreadsheet tool, such as Microsoft Excel, to simplify the calculations and eliminate math errors.The size of the mean value of the data set depends on the size of the standard deviation.Number of hours spent watching television 10 to.82 317.6 635.2 15 to.82 164.4 1,972.8 20 to.82.2 1,407.6 25 to,620 -2.82.0 480.0 30 to,464.18.8 369.6 35 to,406.18.6 1,960.8 40 to.18 148.4 1,187.2 220 6,560 8,013.2 Use the information found in the table above to find the standard.
Note: During calculations, when a variable is grouped by class intervals, the midpoint of the interval is used in place of every other value in the interval.