inlays85k5

2021-11-30

Solve for the mode and range of the given data. Show your solutions on the space provided.
$\begin{array}{|ccc|}\hline Data& Mode& Range\\ 10,7,7,4,5,6,4& 1& 2\\ 4.2,3.9,4.6,5.1,3.8,4.7,3.5& 3& 4\\ 5.1,3.2,4.7,4.0,3.6& 5& 6\\ \hline\end{array}$

### Answer & Explanation

Egreane61

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
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
$Range=\text{Largest value}-\text{smallest value}=10-2=8$
Step 3
1. 10, 7 , 7, 4, 5, 6, 4
First sort the data in ascending order.
4, 4, 5, 6, 7, 7, 10
$\text{Mode}=4,7$
Here we have two modal values as 4 and 7 repeating 2 times.
Range:
Largest value $=10$
Smallest value $=4$
$\text{Range}=10-4=6$
Therefore,
Step 4
2. 4.2, 3.9, 4.6, 5.1, 3.8, 4.7, 3.5
First sort the data in ascending order.
3.5, 3.8, 3.9, 4.2, 4.6, 4.7, 5.1
$Mode=\text{no mode}$
Here every value is repeating only once. So we can say there is no modal value.
Range:
$\text{Largest value}=5.1$
$\text{Smallest value}=3.5$
$\text{Range}=5.1-3.5=1.6$
Therefore, $Mode=\text{no mode and Range}=1.6$
Step 5
3. 5.1, 3.2, 4.7, 4.0, 3.6
First sort the data in ascending order.
3.2, 3.6, 4.0, 4.7, 5.1
$Mode=\text{No mode}$
Here every value is repeating only once. So we can say there is no modal value.
Range:
$\text{Largest value}=5.1$
$\text{Smallest value}=3.2$
$\text{Range}=5.1-3.2=1.9$
Therefore, $\text{Mode}=\text{No mode and Range}=1.9$

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