Question

One way to measure the spread of data is to calculate the range (maximum minus minimum). What range of cell sizes did each sugar grow? Why is the range often not a wetul

measure of spread?
a. Another method for measuring the spread is the average distance to the moan, called the mean absolute deviation Find the distance each value is to the mean (remember to me
absolute value because districes are positivel), and find the mean distance. Compare the mean absoluto deviation of Sugar W to Sugar P.
b. A mean absolute deviation should not be calculated if the data has outliers or is not symmetric. Why?
c. When the data is not symmetric or has outliers, the interquartile range (IQR) can be used to measure spread. Compare the 1QR of the two sugars.

Answer 1

The range, mean absolute deviation and interquartile range are different measures of spread in a dataset, with IQR being more robust in the presence of outliers or asymmetric data.

Step-by-step explanation:

Understanding Measures of Spread in Data

When analyzing the spread of data, the range represents the difference between the maximum and minimum values in the dataset. However, the range can be affected significantly by outliers, hence it is not always the best measure of spread. The mean absolute deviation (MAD) is another measure that calculates the average distance between each data point and the mean, using absolute values to ensure all distances are positive. This measure can be skewed by outliers as well. When there are outliers or the data is not symmetric, it might not be representative of the data's typical deviation.

If the data is not symmetric or contains outliers, the interquartile range (IQR) is a more robust measure as it looks at the middle 50% of the data, reducing the influence of extreme values. To compare IQRs, we would need to find the values of the first quartile (Q1) and the third quartile (Q3) and subtract Q1 from Q3 for each sugar's cell sizes.

Considering the researcher's soda can sugar example, where the mean is 39.01 and the standard deviation is 0.5, we can observe that a small standard deviation indicates the data points are close to the mean, showing low variability. A large standard deviation would suggest a greater spread around the mean. Therefore, the standard deviation provides crucial insights into how spread out the data are about the mean, especially useful in symmetric distributions.