Solve for the mode and range of the given data. Show your solutions on the...

Step 1
Given,
1. 10, 7 , 7, 4, 5, 6, 4
2. 4.2, 3.9, 4.6, 5.1, 3.8, 4.7, 3.5
3. 5.1, 3.2, 4.7, 4.0, 3.6
To find,
Mode and range of the given data sets.
Step 2
Answer:
First we see what is Mode and Range?
Mode:
Mode is the most repeatating value in the data set.
For Example:
1, 2 , 2 , 3 , 5
Here mode is 2
Range;
Range is the difference of largest value and smallest vaue of the given data set.
Ex. 2, 5 , 6, 7, 10
${\displaystyle Range=\text{Largest value}-\text{smallest value}=10-2=8}$
Step 3
1. 10, 7 , 7, 4, 5, 6, 4
Answer:
First sort the data in ascending order.
4, 4, 5, 6, 7, 7, 10
${\displaystyle \text{Mode}=4,7}$
Here we have two modal values as 4 and 7 repeating 2 times.
Range:
Largest value ${\displaystyle =10}$
Smallest value ${\displaystyle =4}$
${\displaystyle \text{Range}=10-4=6}$
Therefore, ${\displaystyle Mode=(4,7)\text{and}Ran\ge =6}$
Step 4
2. 4.2, 3.9, 4.6, 5.1, 3.8, 4.7, 3.5
Answer:
First sort the data in ascending order.
3.5, 3.8, 3.9, 4.2, 4.6, 4.7, 5.1
${\displaystyle Mode=\text{no mode}}$
Here every value is repeating only once. So we can say there is no modal value.
Range:
${\displaystyle \text{Largest value}=5.1}$
${\displaystyle \text{Smallest value}=3.5}$
${\displaystyle \text{Range}=5.1-3.5=1.6}$
Therefore, ${\displaystyle Mode=\text{no mode and Range}=1.6}$
Step 5
3. 5.1, 3.2, 4.7, 4.0, 3.6
Answer:
First sort the data in ascending order.
3.2, 3.6, 4.0, 4.7, 5.1
${\displaystyle Mode=\text{No mode}}$
Here every value is repeating only once. So we can say there is no modal value.
Range:
${\displaystyle \text{Largest value}=5.1}$
${\displaystyle \text{Smallest value}=3.2}$
${\displaystyle \text{Range}=5.1-3.2=1.9}$
Therefore, ${\displaystyle \text{Mode}=\text{No mode and Range}=1.9}$