Question

Using empirical formula, calculate the mode for the following data:
$17$, $16$, $25$, $23$, $22$, $23$, $28$, $25$, $25$, $23$

• A. $14.61$
• B. $19.6$
• C. $23.6$
• D. $28.3$

Answer 1

Answer: (C)

$23.6$

Given data set is $17,16,25,23,22,23,28,25,25,23$

Arranging the data set in ascending order we get

$16,17,22,23,23,23,25,25,25,28$

Total number of values is $10$

Mean is $\frac{16+17+22+23+23+23+25+25+25+28}{10}=\frac{227}{10}=22.7$

Median is the middle value i.e., $\frac{5^{th}+6^{th}}{2}$ value is the median.

Therefore median is $\frac{23+33}{2}=23$

The empirical formula is $mode=3median-2mean$

$⟹mode=3\left(23\right)-2\left(22.7\right)=69-45.4=23.6$