Question:
The average speed of a car running at the rate of 15 km/hour during the first 30 km and at 20 km/hour during the second 30 km and at 25 km/hour during the third 30 km, will be
The average speed of a car running at the rate of 15 km/hour during the first 30 km and at 20 km/hour during the second 30 km and at 25 km/hour during the third 30 km, will be
Updated On: Oct 1, 2023
- 19.15 km/hour
- 20 km/hour
- 19.65 km/hour
- 19.75 km/hour.
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The Correct Option is A
Solution and Explanation
Here, the required average speed is equal to the harmonic mean of the three speeds
$ = \frac{3}{\frac{1}{15} + \frac{1}{20}+ \frac{1}{25}} $ km/hour
$= \frac{3\times300}{20+15+12} = \frac{900}{47} $ km/hour
= 19.15 km/hour.
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Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution