What will be the value of median of a moderately asymmetrical distribution? If the mean and mode are 30 and 24 respectively.
1 answer:
The mean, the median and the mode are measures of central tendency, and they are related in some many ways, depending on the type of distribution.
The median of the moderately asymmetrical distribution is 26
The given parameters are:
For a moderately asymmetrical distribution, the mean, median and mode are related by the following equation:
Substitute known values
Collect like terms
Divide both sides by 3
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Answer:
b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal Variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. Sample of 35:
This means that:
The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Sample of 40:
This means that:
Which of the following best describes the sampling distribution of the difference in mean life span of gas ranges and electric ranges?
Shape is approximately normal.
Mean:
Standard deviation:
So the correct answer is given by option b.