In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each. Some summary statistics: Clare mean: 2,000 grams MAD: 275 grams median: 2,000 grams IQR: 500 grams Lin mean: 2,000 grams MAD: 225 grams median: 1,950 grams IQR: 350 grams Which student was better at estimating the mass of the objects? Explain your reasoning.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each.
Some summary statistics:
Clare
mean : 2,000 grams- MAD: 275 grams
- median: 2,000 grams
- IQR: 500 grams
Lin
- mean: 2,000 grams
- MAD: 225 grams
- median: 1,950 grams
- IQR: 350 grams
Which student was better at estimating the mass of the objects? Explain your reasoning.
Given Information:
In a science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each.
Clare
- mean: 2,000 grams
- MAD: 275 grams
- median: 2,000 grams
- IQR: 500 grams
Lin
- mean: 2,000 grams
- MAD: 225 grams
- median: 1,950 grams
- IQR: 350 grams
Which student was better at estimating the mass of the objects.
Compare summary statistics for both Clare and Lin:
We observe that, mean is same 2000 grams for both.
Median is almost same: Median of Clare is 2000 grams and Median of Lin is 1950 grams which is approximately 2000.
Mean Absolute Deviation (MAD) is a measure of variability or dispersion, it is the average distance between each data value and the mean. It describe the variation in the data. In other words, it indicates how spread out the data values are, from the mean.
MAD - 275 grams vs 225 grams. There is more MAD for Clare's data.
Interquartile Range (IQR) is also a measure of dispersion, it tells how spread out the "middle" values are, or it tells when some of the other values are "too far" from the central value.
IQR- 500 grams vs 350 grams.
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