Vista-gram Basics
What type of graph uses bars to represent the frequency of data in intervals?
A histogram
What is the smallest possible sum when rolling two six-sided dice?
2
What does the mean of a data set represent?
The average value of the data.
What is the probability of rolling a 2 with two dice?
1/36
What does the range of a data set tell you?
The difference between the largest and smallest values.
If the highest bar in a histogram is at the interval 5-10, what does that tell you about the data?
Most of the data values fall between 5 and 10.
What is the largest possible sum when rolling two six-sided dice?
12
What is the median of a data set?
The middle value when the data is ordered.
What is the probability of rolling a 7 with two dice?
6/36 or 1/6
In a histogram of dice rolls, which sum has the lowest frequency?
2 and 12 (each only occurs once).
In a histogram, the interval 10−15 has a frequency of 6. What does the number 6 represent?
6 data points fall within the interval 10−15.
What shape would you expect the histogram of dice sums to have?
A bell shape or symmetric distribution, peaking around 7.
If a histogram is symmetric, how do the mean and median compare?
They are approximately the same.
If you roll two dice 30 times, how many times would you expect to roll a 7?
Approximately 5 times
If you rolled three dice instead of two, how would the histogram shape change?
It would still be symmetric but would peak around a higher sum.
If a histogram has intervals of 0-5, 6-10, and 11-15, what is the width of each bar?
5 units.
How many possible outcomes are there when rolling two six-sided dice?
36 outcomes
Calculate the mean of this data set: 2,4,4,6,8.
4.8
How does increasing the number of trials affect the histogram?
The histogram becomes smoother and more clearly shows the expected (symmetric) pattern.
What type of data set produces a uniform histogram?
A data set where all values have the same frequency.
In a histogram of dice rolls, the interval 6−7 has the highest frequency. What is the most likely sum rolled?
7, since it is the midpoint of the interval with the highest frequency.
Why is 7 the most common sum when rolling two dice?
There are more combinations (6) that produce a sum of 7 than any other sum.
Why might the mean and median differ in a skewed distribution?
The mean is affected by extreme values, while the median is not.
What might cause a real histogram of dice rolls to differ slightly from the expected pattern?
Random variation or a small sample size.
Explain why a histogram of test scores might be skewed.
If most students scored high or low, it creates a skewed distribution, as the frequencies are not symmetric.