Answer:
L= 40, f =30, cf=20,h= 20,N/2=80/2=40------- (Given)
Step-by-step explanation:
First, let's make the frequency table for this question.
[tex]\begin{tabular}{|c|c|c|}\cline{1-3} Class Interval & fi & cf \\\cline{1-3}0 - 20 & 8 & 8 \\\cline{1-3}20 - 40 & 12 & 20\\\cline{1-3}40 - 60 & 30 & 50\\\cline{1-3} 60 - 80 & 20 & 70 \\\cline{1-3}80 - 100 & 10 & 80\\\cline{1-3} \cline{1-3}\end{tabular}[/tex]
Here,
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Now, to find the median, we'll use the below formula.
[tex]\boxed{\sf Median = l \ + (\dfrac{\dfrac{n}{2} - cf}{f}) h }[/tex]
Let's apply the formula and find the median.
⇒ Median = [tex]\sf l \ + (\dfrac{\dfrac{n}{2} - cf}{f}) h[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{\dfrac{80}{2} - 20}{30}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{40 - 20}{30}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{20}{30}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{2}{3}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + \dfrac{40}{3}[/tex]
⇒ Median = 40 + 13.33
⇒ Median = 53.33
∴ The median of the following data is 53.33.
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Answers & Comments
Answer:
L= 40, f =30, cf=20,h= 20,N/2=80/2=40------- (Given)
Step-by-step explanation:
Verified answer
First, let's make the frequency table for this question.
[tex]\begin{tabular}{|c|c|c|}\cline{1-3} Class Interval & fi & cf \\\cline{1-3}0 - 20 & 8 & 8 \\\cline{1-3}20 - 40 & 12 & 20\\\cline{1-3}40 - 60 & 30 & 50\\\cline{1-3} 60 - 80 & 20 & 70 \\\cline{1-3}80 - 100 & 10 & 80\\\cline{1-3} \cline{1-3}\end{tabular}[/tex]
Here,
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Now, to find the median, we'll use the below formula.
[tex]\boxed{\sf Median = l \ + (\dfrac{\dfrac{n}{2} - cf}{f}) h }[/tex]
Here,
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Let's apply the formula and find the median.
⇒ Median = [tex]\sf l \ + (\dfrac{\dfrac{n}{2} - cf}{f}) h[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{\dfrac{80}{2} - 20}{30}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{40 - 20}{30}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{20}{30}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + (\dfrac{2}{3}) \times 20[/tex]
⇒ Median = [tex]\sf 40 \ + \dfrac{40}{3}[/tex]
⇒ Median = 40 + 13.33
⇒ Median = 53.33
∴ The median of the following data is 53.33.
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