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
Tags: Measures of Central Tendency(Part-4)| Giri Banarjee Statistics Solution| Problems on Mean