Measures of Central Tendency(Part-5)| Giri Banarjee Statistics Solution| Problmes on Mean Median Mode

Q34. If the relation between two variables $\small$ and $\small y$ is $\small xy=2$, find the relation between harmonic mean of $\small x$ and arithmetic mean of $\small y$.

Ans: 

Hints:

$\small H.M(x)$=$\small \frac{1}{\sum_{i=1}^{n}(\frac {1}{x_{i}})}$

 

$\small \bar y$=$\frac{1}{n} \sum_{i=1}^{n} y_{i}$.

 

Now put $\small y_{i}$=$\small \frac{2}{x_{i}}$

 

Q35.Mention the situations in which the arithmetic mean is unsuitable as an average.

 

Ans: The situations where you can use Median or Mode as  the best average method.

 

Q36. Appropriate measure of these followings:

(i)    Frequency distribution of size of footwears sold in a shop 

 

Ans:Mode

(ii)   Rate of population increase

 

Ans:G.M

 

(iii)  Life hours of sample of 80 lamps

 

Ans:A.M

 

(iv)  Speed to cover a fixed distance

 

Ans:H.M 

(v)   Monthly income of advocates in city.

 

Ans:  Median

Q37.Find the weighted arithmetic mean and weighted harmonic mean of first $\small n$ integers, when in each case are proportional to the corresponding value.

 

Ans: 

$\small x_{i}$ are $\small 1,2,3,.....,n$, and the weights are $\small f_{i}$'s are $\small 1.,2,3,....n$. Now find the weighted (arithmetic/harmonic) mean.

Q38.

Q39.Practical Problem

Q40.Practical Problem

Q41.Practical Problem

 

Q42.Practical Problem

 

Q43.Practical Problem

 

Q44.Practical Problem

 

Q45.Practical Problem

 

Q46.A covered a distance of 50 kms.four times the; the first time at 50 km/h, second time at 20 km/h, third time at 40 km/h, fourth time at 25 km/h. Using appropriate average speed of the car.

 

Ans: Use Harmonic Mean: 

=$\small \frac{50}{\frac{1}{50}+\frac{1}{20}+\frac{1}{40}+\frac{1}{25}}$

 

Q47.In a batch of 15 students 5 students failed in a test.The marks of 10 students who passed were 90,60,70,80,80,90,60,50,40,70. Find the median of the marks of all the 15 students.

 

Ans: 

The median is $\small (\frac{n+1}{2})$the value of the observations.

Here, n=15

So, $\small 8th$ observation is the median value.

At first we have to rearrange the values of 15 students who passed the examination

 

1. 1st student: $\small x_{1}$[Fail] 

2. 2nd student: $\small x_{2}$[Fail] 

3. 3rd student: $\small x_{3}$[Fail]

4. 4th student: $\small x_{2}$[Fail] 

5. 5th student: $\small x_{2}$[Fail] 

6. 6th student: $\small 40$[Pass] 

7. 7th student: $\small 50$[Pass] 

8. 8th student: $\small 60$[Pass][Median value]

 

Q48.Practical Problem

 

 

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