The length of a metal block is measured 4 times using a ruler. The results are shown below: measurement # length l (mm) 1 23.5 2 23.8 3 23.2 4 23.6 First, calculate the mean length and fill it in the blank below. Next, fill in the blanks for the differences and in the table above. Finally, calculate the standard deviation, the standard deviation of the mean and the 2σ uncertainty and fill in the blanks below. Important notes (read before entering your answers): Enter the values in mm using decimal notation (e.g. 0.0123). A leading zero before the decimal point must be entered (e.g. 0.0123, not .0123). Do not use scientific notation, as it will not be recognized, and do not enter the units. Do not round the numbers, as this may cause rounding errors to accumulate. Mean length: mm Standard deviation mm Standard deviation of the mean mm 2σ uncertainty mm
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.
The length of a metal block is measured 4 times using a ruler. The results are shown below:
| measurement # | length l (mm) | ||
| 1 | 23.5 | ||
| 2 | 23.8 | ||
| 3 | 23.2 | ||
| 4 | 23.6 |
- First, calculate the
mean length and fill it in the blank below. - Next, fill in the blanks for the differences and in the table above.
- Finally, calculate the standard deviation, the standard deviation of the mean and the 2σ uncertainty and fill in the blanks below.
Important notes (read before entering your answers):
- Enter the values in mm using decimal notation (e.g. 0.0123).
- A leading zero before the decimal point must be entered (e.g. 0.0123, not .0123).
- Do not use scientific notation, as it will not be recognized, and do not enter the units.
- Do not round the numbers, as this may cause rounding errors to accumulate.
| Mean length: | mm | |
| Standard deviation | mm | |
| Standard deviation of the mean | mm | |
| 2σ uncertainty | mm |
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
