Question

find the mean, median, mode, and range for each set of numbers.
2 1 1 5 6
median -
mode -
range -
mean -
7 7 0 14 0 7 14
median -
mode -
range -
mean -

Explanation:

Step1: Sort the first set of numbers

Sort \(2,1,1,5,6\) as \(1,1,2,5,6\).

Step2: Calculate the median of the first set

The median is the middle number. For \(n = 5\) (odd), median is the \(\frac{n + 1}{2}\) -th number. \(\frac{5+1}{2}=3\) -rd number. So median \(=2\).

Step3: Calculate the mode of the first set

The mode is the most frequent number. Here \(1\) appears twice. So mode \(=1\).

Step4: Calculate the range of the first set

Range \(=\text{Max}-\text{Min}\). Max \(=6\), Min \(=1\). Range \(=6 - 1=5\).

Step5: Calculate the mean of the first set

Mean \(=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). \(\sum_{i=1}^{5}x_{i}=1 + 1+2+5+6=15\), \(n = 5\). Mean \(=\frac{15}{5}=3\).

Step6: Sort the second set of numbers

Sort \(7,7,0,14,0,7,14\) as \(0,0,7,7,7,14,14\).

Step7: Calculate the median of the second set

For \(n = 7\) (odd), \(\frac{n + 1}{2}=4\) -th number. Median \(=7\).

Step8: Calculate the mode of the second set

The mode is the most frequent number. \(7\) appears three times. So mode \(=7\).

Step9: Calculate the range of the second set

Max \(=14\), Min \(=0\). Range \(=14-0 = 14\).

Step10: Calculate the mean of the second set

\(\sum_{i=1}^{7}x_{i}=0+0 + 7+7+7+14+14=49\), \(n = 7\). Mean \(=\frac{49}{7}=7\).

Answer:

First set:
Median - \(2\)
Mode - \(1\)
Range - \(5\)
Mean - \(3\)

Second set:
Median - \(7\)
Mode - \(7\)
Range - \(14\)
Mean - \(7\)