Measures of Center & Distributions
What is mean, median and mode?
These percentages roughly represent the percent of the data values that fall within one, two, and three standard deviations from the mean of a normal distribution.
What is 68%-95%-99.7%
A data set is normally distributed with a mean of 50 and a standard deviation of 10. What is the z-score of the data value 60?
What is 1?
The area to the left of a z-score of -1.73 is this.
What is .0418?
This measure of center can be found by arranging the data values from least to greatest and then finding the middle value.
What is the median?
A normal distribution has a mean of 15 and a standard deviation of 3. The value that is 2 negative standard deviations away from the mean is this.
What is 9?
Josiah scored 1300 on the SAT. The mean of the SAT is 1000 and the standard deviation is 200. This is the z-score of Josiah's SAT score.
What is 1.5?
The area to the right of a z-score of 0.62 is this.
1 - 0.7324 = 0.2676
Find the three measures of center for the data set:
{0, 3, 5, 5, 6, 7, 10, 12}
Mean= 6
Median = 5.5
Mode = 5
A normal distribution has a mean of 24 and a standard deviation of 6. 68% of the values of this distribution fall between what two data values?
What is 18 and 30?
Sadie scored 28 on the ACT. If the mean of SAT scores is 21 and the standard deviation is 5, this is Sadie's z-score.
What is 1.4?
The weight of chocolate bars from a particular chocolate factory has a mean of 8 ounces with standard deviation of 0.1 ounce. What is the percent of bars that weigh less than 8.17 ounces?
95.54%
a) Draw a histogram for a set of data that is SKEWED RIGHT.
b) Which measure of center BEST describes this data set?
a) Histograms should have most of the data on the LEFT side.
b) Median
A normal distribution has a mean of 100 and a standard deviation of 10. The percentage of data values that fall between the values of 70 and 90 is this.
What is 15.85%?
Adin scored 1400 on the SAT and Gabriel scored 25 on the ACT. The mean SAT score is 1000 and the standard deviation is 200. The mean ACT score is 21 and the standard deviation is 5. This is the better score.
What is 1400?
A group of friends compare what they received while trick or treating. They find the average number of peices of candy received is 43, with a standard deviation of 5. What is the percent of friends who received more than 50 pieces of candy?
100 - 91.92 = 8.08%
Explain why the MEAN is not a good measure of center for this data set. What measure would be better to use in this case?
{4, 5, 7, 7, 8, 10, 45}
There is an outlier, 45, which would pull the mean farther right (larger) than it should be.
The median is a better measure of center.
A normal distribution has a mean of 10 and a standard deviation of 1. The percentage of data values that fall between the values of 8 and 12 is this.
What is 95%?
The mean of a normal distribution is 10 and the standard deviation is 2. The z-score of a data value is 3. This is the data value.
What is 16?
A particular leg bone for dinosaur fossils has a mean length of 5 feet with standard deviation of 3 inches. What is the percent of bones that have lengths between 59 and 62 inches?
74.86% - 37.07% = 37.79%