The mode of the following frequency distribution is 38. Find the value of x.
| Runs scored | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Number of students | 7 | 9 | 12 | 16 | x | 6 | 11 |
Given,Value of Mode = 38
and the class of Mode is between 30 to 40 or 30-40
We Know that,
Model = `l+\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h`
⇒ 38 = 30 + `"16 - 12"/"32 -12- x"` `\times`10
⇒ 38 - 30 = `"4"/"20- x"` `\times`10
⇒ 8 = `"4"/"20- x" ``\times`10
⇒ 8 (20 - x) = 40
⇒ 20 - x = `40/8`
⇒ 20 - x = 5
⇒ 20 - 5 = x
⇒ 15 = x
∴ x = 15