# Data from the scores of the 100 Student Quantitative Methodalogy have

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

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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,
$\begin{array}{|c|c|c|} \hline Quantity&Amount(f)&Cumulative\ amount&x&fx\\ \hline 31-40&5&5&35.5&177.5\\ \hline 41-50&8&13&45.5&364\\ \hline 51-60&12&25&55.5&666\\ \hline 61-70&17&42&65.5&1113.5\\ \hline 71-80&25&67&75.5&1887.5\\ \hline 81-90&21&88&85.5&1795.5\\ \hline 91-100&12&100&95.5&1196\\ \hline &\sum A=100\\ \hline \end{array}$
Summation of fx is given by,
$$\displaystyle\sum{f}_{{{i}}}{x}_{{{i}}}={7150}$$
The mean is given by,
$$\displaystyle\overline{{{x}}}={\frac{{\sum{f}_{{{i}}}{x}_{{{i}}}}}{{\sum{f}}}}$$
$$\displaystyle={\frac{{{7150}}}{{{100}}}}$$
$$\displaystyle={71.5}$$
Median is given by,
$$\displaystyle={L}+{\left[{\frac{{{\left({\frac{{{N}+{1}}}{{{2}}}}\right)}-{\left({F}+{1}\right)}}}{{{f}_{{{m}}}}}}\right]}\cdot{h}$$
Where,
$$\displaystyle{L}={71}$$
$$\displaystyle{N}={100}$$
$$\displaystyle{F}={42}$$
$$\displaystyle{h}={9}$$
$$\displaystyle{f}_{{{m}}}={25}$$
$$\displaystyle{M}{e}{d}{i}{a}{n}={71}+{\frac{{{55.5}-{43}}}{{{25}}}}\cdot{9}$$
$$\displaystyle={75.5}$$
Mode is given by,
$$\displaystyle={L}+{\frac{{{f}_{{{0}}}-{f}_{{{1}}}}}{{{2}{f}_{{{0}}}-{f}_{{{1}}}-{f}_{{{2}}}}}}\cdot{h}$$
$$\displaystyle{f}_{{{0}}}={25}$$
$$\displaystyle{f}_{{{1}}}={17}$$
$$\displaystyle{f}_{{{2}}}={21}$$
$$\displaystyle{M}{o}{d}{e}={71}+{\frac{{{25}-{17}}}{{{2}\times{25}-{17}-{21}}}}\cdot{9}$$
$$\displaystyle={77}$$
So mean, median and mode of this grouped data is 71.5, 75.5 and 77 respectively.