Question

please any one answer this question with required steps and process...if it is proper I will mark u as Brainlist​

Answer 1

Answer:

y = 5 and x = f - 43 (where f is sum of all frequencies)

Step-by-step explanation:

Given: Mode = 55

Data is given in Grouped Frequency Distribution table.

This mean give mode is of continuous series.

Formula of Mode of Continuous series is given by,

Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times hMode=l+2f1−f0−f2f1−f0×h

where, l = lower limit of modal class

           h = Width/length of modal class

           f_1f1 = frequency of modal class

           f_0f0 = frequency of class preceding modal class

           f_2f2 = frequency of class succeeding  modal class

Here, Modal class is 45 - 60 (because mode lies in this class interval)

⇒ l = 45 , h = 15 , f_1f1 = 15 , f_0f0 = y , f_2f2 = 10

substituting these values in formula, we get

55=45+\frac{15-y}{2\times15-y-10}\times 1555=45+2×15−y−1015−y×15

55-45=\frac{15-y}{20-y}\times 1555−45=20−y15−y×15

10=\frac{15-y}{20-y}\times 1510=20−y15−y×15

\frac{10}{15}=\frac{15-y}{20-y}1510=20−y15−y

\frac{15-y}{20-y}=\frac{2}{3}20−y15−y=32

3\times(15-y)=2\times(20-y)3×(15−y)=2×(20−y)

45-3y=40-2y45−3y=40−2y

-3y+2y=40-45−3y+2y=40−45

-y=-5−y=−5

y=5y=5

To find Value of x we should know sum of all frequencies.

Let say sum of all frequencies be f

so, steps to find value of x

Sum of all frequencies = f

6 +7 + y + 15 + 10 + x = f

6 + 7 + 5 + 15 +10 + x = f

x + 43 = f

x = f - 43

Therefore, Value of x is (sum of frequencies) - 43.