Harold Kessler

2021-12-10

Data from the scores of the 100 Student Quantitative Methodalogy have been compiled in the frequency distribution table below:
$\begin{array}{|cc|}\hline \text{Value of Quantitative Methodology}& \text{amount}\\ 31-40& 5\\ 41-50& 8\\ 51-60& 12\\ 61-70& 17\\ 71-80& 25\\ 81-90& 21\\ 91-100& 12\\ & 100\\ \hline\end{array}$
Based on the data above, calculate:
a. Mean
b. Median
c. Mode

Stuart Rountree

Step 1:Given
The table shows the distribution of various classes.
Step 2:Objective
To calculate mean ,median and mode of this table.
Step 3: Solution
The table is as shown below,

Summation of fx is given by,
$\sum {f}_{i}{x}_{i}=7150$
The mean is given by,
$\stackrel{―}{x}=\frac{\sum {f}_{i}{x}_{i}}{\sum f}$
$=\frac{7150}{100}$
$=71.5$
Median is given by,
$=L+\left[\frac{\left(\frac{N+1}{2}\right)-\left(F+1\right)}{{f}_{m}}\right]\cdot h$
Where,
$L=71$
$N=100$
$F=42$
$h=9$
${f}_{m}=25$
$Median=71+\frac{55.5-43}{25}\cdot 9$
$=75.5$
Mode is given by,
$=L+\frac{{f}_{0}-{f}_{1}}{2{f}_{0}-{f}_{1}-{f}_{2}}\cdot h$
${f}_{0}=25$
${f}_{1}=17$
${f}_{2}=21$
$Mode=71+\frac{25-17}{2×25-17-21}\cdot 9$
$=77$
So mean, median and mode of this grouped data is 71.5, 75.5 and 77 respectively.

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