10 pages/≈2750 words
Mathematics & Economics
Module 3 Case Frequency Distribitions (Math Problem Sample)
All problems need to include all required steps and answers and all answers need to be reduced to the lowest terms. Please see instructions.source..
TITLE OF PROJECT
1 The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
1 34Â Â Â 86Â Â Â 57Â Â Â 73Â Â Â 85Â Â Â 91Â Â Â 93Â Â Â 46Â Â Â 96Â Â Â 88Â Â Â 79Â Â Â 68Â Â Â 85Â Â Â 89
To answer this item, first we need to compute for standard deviation. We will use this formula.
We will compute this formula in 4 steps.
Step 1: Find the mean.
Mean = (99+34+86+57+73+85+91+93+46+96+88+79+68+85+89) / 15
Mean = 77.9333.
Step 2:Â Create the following table.
(data - mean)2
Step 3:Â Find the sum of numbers in the last column to get.
Step 4:Â CalculateÂ ÏƒÂ using the above formula.
Using the mean and standard deviation of these scores we can now get the z-score for each grade using this formula:
Z value = (X - Âµ) / Ïƒ
Where, X = Standardized Random Variable,
Âµ = Sample Mean,
Ïƒ = Sample Standard Deviation.
The table below summarizes the z-score for each math grade
There are 11 math grades that are within one (1) standard deviation away from the mean while 14 math grades are within two (2) standard deviations away from the mean. All math grades are within three (3) standard deviations away from the mean.
1 The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
Step 1: Sketch the curve.
The probability thatÂ X>85Â is equal to the blue area under the curve.
SinceÂ Î¼=74.8Â andÂ Ïƒ=7.57Â we have:
PÂ (Â X>85Â )=PÂ (Â Xâ€’Î¼>85â€’74.8Â )=PÂ (Â Xâ€’Î¼Ïƒ>85â€’74.87.57)
SinceÂ Z=xâ€’Î¼ÏƒÂ andÂ 85â€’74.87.57=1.35Â we have:
PÂ (Â X>85Â )=PÂ (Â Z>1.35Â )
Step 3:Â Use the standard normal table to conclude that:
0.0885 x 100 = 8.85%
Only 8.85% of the class (or one person) scored above 85% for Math test #3.
2 If you know the standard deviation, how do you find the variance?
Get the Whole Paper!
Not exactly what you need?
Do you need a custom essay? Order right now:
- Frequency DistributionsDescription: The number of vacation days taken by employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. ...1 page/≈275 words | No Sources | APA | Mathematics & Economics | Math Problem |
- Case Measures of Central TendencyDescription: The measures of central tendency are measures of location and include the mean, mode and median and all are suitable under different situations....10 pages/≈2750 words | No Sources | APA | Mathematics & Economics | Math Problem |
- Basic Statistics Module 2 CaseDescription: Therefore, measure of central tendency is a single value that describes a given set of data by sorting out the central position within that set of data...10 pages/≈2750 words | No Sources | APA | Mathematics & Economics | Math Problem |