Question

number showing on a rolled die (data from 24 rolls)
5 - # - summary:
min: __ q1: med: q3: max: __
the mean is __ which is __ than the median
the shape of this data set is ____
outcome_when_rolling_a_die_24_times

Explanation:

Step1: Arrange data in ascending - order

The data points are the results of 24 die - rolls. Since a die has values from 1 to 6, and looking at the dot - plot, we assume the full set of data values. The data set in ascending order: 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6.

Step2: Find the 5 - number summary

• Min: The smallest value in the data set is 1.
• Q1: The first quartile. Since $n = 24$, the position of Q1 is $\frac{n + 1}{4}=\frac{24+1}{4}=6.25$. The 6th value is 2 and the 7th value is 2, so Q1 = 2.
• Med: The median. Since $n = 24$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values. $\frac{n}{2}=12$ and $\frac{n}{2}+1 = 13$. The 12th value is 3 and the 13th value is 4, so Med=$\frac{3 + 4}{2}=3.5$.
• Q3: The third quartile. The position of Q3 is $\frac{3(n + 1)}{4}=\frac{3\times(24 + 1)}{4}=18.75$. The 18th value is 5 and the 19th value is 5, so Q3 = 5.
• Max: The largest value in the data set is 6.

Step3: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. $\sum_{i=1}^{24}x_{i}=1\times4+2\times4+3\times4+4\times4+5\times4+6\times4=(1 + 2+3+4+5+6)\times4=\frac{6\times(6 + 1)}{2}\times4=84$. So $\bar{x}=\frac{84}{24}=3.5$.

Step4: Determine the shape

Since the mean = median = 3.5, the shape of the data set is symmetric.

Answer:

Min: 1
Q1: 2
Med: 3.5
Q3: 5
Max: 6
The mean is 3.5 which is equal to the median
The shape of this data set is symmetric