Question

If the median and the mode of a set of data are 12 and 15, respectively, then find the value of thrice the mean of the same data set.

• A. $$\frac{33}{2}$$
• B. $$\frac{63}{2}$$
• C. $$\frac{23}{2}$$
• D. $$\frac{35}{2}$$

Answer 1

Answer:

$$\frac{63}{2}$$

Solution:

Given:

Median is 12 

Mode is 15 

Formula used:

Mode = 3 Median - 2 Mean 

Calculation:

Here, we have median = 12 and mode = 15 

As, we know that 

Mode = 3 median - 2mean

 

⇒ 15 = 3 ( 12) - 2 mean 

⇒ 15 = 36 - 2mean 

Mean = $\frac{21}{2}$

 

Now, thrice of mean = $3\times{\frac{21}{2}}$ = $\frac{63}{2}$

 

Hence, the required value of thrice the mean is $\frac{63}{2}$ .