Question

please solve this question ​

Answer 1

Step-by-step explanation:

Solution :-

Finding Mean :-

See the above attachment

Step Deviation Method:-

From the first table we have,

Assumed Mean (A) = 45

Sum of all frequencies (∑fi) = 146

∑fiui = -142+122 = -20

Size of the class (h) = 10

We know that

Mean = A + ( ∑ fiui / ∑fi) × h

On Substituting the values in the above formula then

=> Mean = 45 + (-20/146)×10

=> Mean = 45 + [(-20×10)/146]

=> Mean = 45 + (-200/146)

=> Mean = 45 + ( - 1.36)

=> Mean = 45 - .36

=> Mean = 43.64

Finding the Median :-

See the above attachment

From the second table we have,

Sum of all observations (N) = 146

N/2 = 146/2 = 73

Median class =40-50

Lower boundary of the median class (l) = 40

Cumulative frequency of the class preceding the median class (cf) = 68

Frequency of the median class (f) = 18

Size of the class (h) = 10

We know that

Median (M) = l + [{(n/2)-cf}/f] × h

On Substituting the values in the above formula then

=> M = 40 + [ (73-68)/18]×10

=>M = 40+[(5/18)×10]

=> M = 40 + [(5×10)/18]

=> M = 40 + (50/18)

=> M = 40+(25/9)

=> M = 40+2.77

=> M = 42.77

Finding the Mode :-

See the above attachment

From the third table we have,

Modal class = 30-40

Lower boundary of the modal class (l) = 30

Frequency of the modal class (f1) = 28

Frequency of the class preceding the modal class (f0) = 17

Frequency of the class succeeding the modal class (f2) = 18

Size of the class (h) = 10

We know that

Mode (z) = l +[(f1-f0)/(2f1-f0-f2)]×h

On Substituting the values in the above formula then

=> z = 30+[(28-17)/(2×28-17-18)]×10

=>z = 30+[11/(56-35)×10]

=>z = 30+[11/21)×10]

=>z = 30+(110/21)

=> z = 30+5.23

=> z = 35.23

Relationship among mean ,median and mode:-

We have

Mean = 43.64

Median = 42.77

Mode = 35.23

We know that

Mode = 3×Median - 2×Mean

=3×Median - 2×Mean

=> 3(42.77)-2(43.64)

=> 128.31-87.28

=> 41.03

=> Mode = 41.03

This is closely related to the value .

Used formulae:-

• Mean =A + ( ∑ fiui / ∑fi) × h

• A = Assumed Mean

• ∑fi = Sum of all frequencies

• Median (M) = l + [{(n/2)-cf}/f] × h

• N = Sum of all observations

• l=Lower boundary of the median class

• cf=Cumulative frequency of the class preceding the median class

• f = Frequency of the median class

• Mode (z) = l +[(f1-f0)/(2f1-f0-f2)]×h

• l=Lower boundary of the modal class

• f1=Frequency of the modal class

• f0=Frequency of the class preceding the modal class

• f2 = Frequency of the class succeeding the modal class

• h = Size of the class