a. Compute the mean, median, and mode.
b. Compute the variance, standard deviation, range, coefficient
of variation, and Z scores. Are there any outliers?
Explain.
c. Are the data skewed? If so, how?
d. Based on the results of (a) through (c), what conclusions
can you reach concerning the total fat of chicken
sandwiches?
Here is some info.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll have to let you do the calculations.
To answer these questions, I need the dataset of total fat values for chicken sandwiches. Please provide the dataset so that I can help you compute the statistics and draw conclusions.
To compute the mean, median, and mode, you need the data set of total fat values for chicken sandwiches. Let's assume you have the data set available.
a. To find the mean or average, sum up all the values in the data set and divide by the total number of values. For example, if you have the following values: 20, 25, 25, 30, and 35, you would add them up and divide by 5, resulting in a mean of 27.
To find the median, you have to arrange the data set in ascending or descending order and find the middle value. If you have an odd number of values, it's the exact middle value. If you have an even number of values, take the average of the two middle values. For example, if you have the values: 20, 25, 25, 30, and 35, the median would be 25.
The mode represents the value that appears most frequently in the data set. If there is no value that appears more than once, the data set is said to have no mode.
b. Variance measures the spread or dispersion of the data set. To compute variance, you need to find the average of the squared differences from the mean. It provides information about how far the values are spread out from the mean.
Standard deviation is the square root of the variance. It measures the average amount of variation or dispersion in the data set. It is useful for understanding the consistency or variability of the values.
Range simply calculates the difference between the largest and smallest values in the data set. It gives an idea of how wide the range of values is.
Coefficient of variation is the ratio of the standard deviation to the mean. It is a relative measure of variability that allows the comparison of dispersion between different data sets.
Z scores indicate how many standard deviations a value is from the mean. It provides information about how extreme or unusual a value is within the data set.
To determine if there are any outliers in the data set, you can use the Z score. Typically, any value that falls more than three standard deviations away from the mean is considered an outlier.
c. To assess if the data is skewed, you need to examine the distribution of the data set. Skewness refers to the asymmetry of the distribution. If the data is skewed, it means that there is a longer tail on one side of the distribution compared to the other. Positive skewness indicates a longer tail on the right, while negative skewness indicates a longer tail on the left.
You can use graphical methods, such as histograms or box plots, to visually assess the skewness. Additionally, statistical tests, like the skewness coefficient, can provide numerical measures of skewness.
d. Based on the results of (a) through (c), you can draw conclusions about the total fat of chicken sandwiches. For example, you can say whether the average fat content is higher or lower, whether there are any common fat values in the data set, and if there are any extreme or outlier values. Additionally, you can determine if the data is skewed, and in which direction.
Remember, to actually obtain the answers, you would need the specific data set of total fat values for chicken sandwiches.