If mean of the data 11, 17, x + 1, 3x, 19, 2x – 4, x + 5 is 21. then find the mode of the data.

Correct option is C

Given:

Data: 11, 17, x + 1, 3x, 19, 2x – 4, x + 5​

Mean: 21

Formula used: 

Mean = $$\frac{ Sum \ of \ all \ observations}{Number\ of \ observations}$$

Solution:

All data points 

11, 17, x + 1, 3x, 19, 2x – 4, x + 5 = 7x +49

Number of data points: 7 

​$$\frac{7x +49}{7}$$ = 21

7x + 49 = 147 

7x = 98

x = 14

Substitute x = 14 into the data:

14 + 1 = 15

3 $$\times$$​14 = 42

2$$\times$$​14 -4 = 24 

14 + 5= 19

Now, data set: 11, 17, 15, 42, 19, 24, 19  

So, 

Mode = 19 

Thus, correct option (c)