All High School Math Resources
Example Questions
Example Question #1 : How To Find Z Scores For A Data Set
What is the -score for a value of 115 when the mean of the population is 103 and the standard deviation is 8?
A -score indicates whether a particular value is typical for a population or data set. The closer the -score is to 0, the closer the value is to the mean of the population and the more typical it is. The -score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.
Example Question #1 : Basic Statistics
A value has a -score of . The value is . . .
two standard deviations from the population mean
below the population mean
one standard deviation from the population mean
the same as the population mean
above the population mean
below the population mean
The -score indicates how close a particular value is to the population mean and whether the value is above or below the mean. A positive -score is always above the mean and a negative -score is always below it. Here, we know the value is below the mean because we have a negative -score.
Example Question #1 : Z Distribution
A population of values has a mean of 43 and a standard deviation of 12. One of the values in the population is 49. What is the Z-score for that value?
A Z-score indicates whether a particular value is typical for a population or data set. The closer the Z-score is to 0, the closer the value is to the mean of the population and the more typical it is. The Z-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.
Example Question #1 : Dependence And Independence
In a standard deck of cards, with replacement, what is the probability of drawing two Ace of Hearts?
Probability of drawing first ace of hearts:
Probability of drawing second ace of hearts:
Multiply both probabilities by each other:
Example Question #4 : Graphing Data
In a standard deck of cards, without replacement, what is the probability of drawing three kings?
Start with 52 cards, probability of drawing first king:
Now you have 51 cards. Probability of drawing second king:
Now you have 50 cards. Probability of drawing third king:
Multiply all probabilities:
Example Question #1 : Identifying Variables And Relationships
With a standard deck of cards, what is the probability of picking a spade then a red card if there is no replacement?
In a standard deck of cards:
Example Question #1 : Probability
Using a standard deck of cards, what is the probability of choosing a single face card?
There are cards in a standard deck: cards in suits. There are face cards (King, Queen, Jack) in each suit, so there are total face cards.
Thus the probability of choosing a single face card is or .
Example Question #1 : Basic Statistics
Range
Median
Mean
Interquartile range
Mode
Median
A box and whisker plot separates the data into quartiles so that each quartile has an equal number of data points. The box indicates the interquartile range, that is, the top line of the box is the third quartile and the bottom line of the box is the second quartile. The line separating the second and third quartiles indicates the median. The lines outside of the box indicate the outer-quartiles (first and fourth).
Example Question #2 : Graphing Data
Based on the scatter plot below, is there a correlation between the and variables? If so, describe the correlation.
Yes; negative exponential relationship
Yes; negative linear relationship
No; there is no correlation
Yes; positive linear relationship
Yes; negative linear relationship
The data points follow an overall linear trend, as opposed to being randomly distributed. Though there are a few outliers, there is a general relationship between the two variables.
A line could accurately predict the trend of the data points, suggesting there is a linear correlation. Since the y-values decrease as the x-values increase, the correlation must be negative. We can see that a line connecting the upper-most and lower-most points would have a negative slope.
An exponential relationship would be curved, rather than straight.
Example Question #1 : How To Find The Range For A Set Of Data
Six homes are for sale and have the following dollar values in thousands of dollars:
535
155
305
720
315
214
What is the range of the values of the six homes?
The range is the simplest measurement of the difference between values in a data set. To find the range, one simply subtracts the lowest value from the greatest value, ignoring the others. Here, the lowest value is 155 and the greatest is 720.