Reorder the numerals in the set, from least to greatest.

\(\displaystyle \{12, 12, 14, 17, 20\}\)

The number in the middle is the median. \(\displaystyle \{12, 12, \mathbf{14}, 17, 20\}\)

The most frequent numeral is the mode. \(\displaystyle \{\mathbf{12}, \mathbf{12}, 14, 17, 20\}\)

The mean is the sum of the numerals divided by the number of data points.

\(\displaystyle \frac{12+12+14+17+20}{5}=15\)

The mean is 15.

The range is the difference between the maximum and the minimum.

\(\displaystyle 20-12=8\)

The range is 8.

Put the data in order from smallest to largest and then calculate each stastic:  mean, mode, median, range

\(\displaystyle 2,\;3,\;5,\;7,\;9,\;9,\;10,\;12,\;15\)

\(\displaystyle Range = Max - Min\) or \(\displaystyle 15-2=13\)

Mode is the most often repeated number or \(\displaystyle 9\)

Median is the number in the middle or \(\displaystyle 9\)

Mean is the sum of the data divided by the number of data points or \(\displaystyle \frac{\sum x}{n}= \frac{72}{9}=8\)

\(\displaystyle \textup{As the numbers are already listed in increasing order, the median is simply}\)

\(\displaystyle \textup{the one in the middle. In this case 8 is the 6th term counted from either side..}\)

The first step to finding the median is always to put the numbers in the proper order:

3, 6, 7, 8, 11, 19, 27, 30, 39, 42

When we have an even amount of numbers, we find the average (or mean) of the middle two to get the median:

11 + 19 = 30/2 = 15

In a standard deck of playing cards we have:

\(\displaystyle 26\; red+26\; black=52\; cards\)

So the probability of picking the first card red is \(\displaystyle \frac{26}{52}=\frac{1}{2}\).

Then the probability of picking the second card black is \(\displaystyle \frac{26}{51}\) because this is without replacement.

They are independent events so the probabilities get multiplied together to give \(\displaystyle \frac{13}{51}\).

First, put the data in order, smallest to largest:

\(\displaystyle 2,3,3,4,5,7,8,9,10,11,15\)

\(\displaystyle mean = \frac{\sum x}{n}=\frac{77}{11}=7\)

\(\displaystyle mode=3\)

\(\displaystyle median = 7\)

\(\displaystyle range=max-min=15-2=13\)

Note, the mode is the number most often repeated in the data set and the median is the middle number.

So \(\displaystyle mean=median\) is the only true statement.

The mean is calculated by adding all the values in a group, then dividing the sum by the total number in the group. 

\(\displaystyle 78+85+82+84+82+79+80=570\)

\(\displaystyle 570/7=81.43\)

The mode is the number that appears most frequently in a series of numbers.  First, organize the numbers in order from least to greatest.  Then, identify the value that is repeated most frequently.

\(\displaystyle 78, 79, 80, 82, 82, 84, 85\)

The median is determined by ordering the values in the group from least to greatest and identifying the value directly in the middle.  For instance, if five numbers are ordered from least to greatest, the third is the median. 

\(\displaystyle 78, 79, 80, 82, 82, 84, 85\)

The sample space for rolling two six-sided dice is \(\displaystyle 36\).

The odd numbers less than seven are one, three, and five.

The smallest sum you can get with two dice is \(\displaystyle 2\).

sum of \(\displaystyle 3:\; \; 1,2\; \;\; 2,1\)

sum of \(\displaystyle 5:\; 1,4\; \; \; 2,3\; \; \; 3,2\; \; \; 4,1\)

\(\displaystyle P(1)+P(3)+P(5)=0+\frac{2}{36}+\frac{4}{36}=\frac{6}{36}=\frac{1}{6}\)