Question: You know the minimum, the maximum, and the 25th, 50th, and 75th percentiles of a distribution. Wh...
You know the minimum, the maximum, and the 25th, 50th, and 75th percentiles of a distribution. Which of the following measures of central tendency or variability can you determine? mean, median, mode, trimean, geometric mean, range, interquartile range, variance, standard deviation
4 answers posted, which one is the right one?
---1---
the given mimimum,maximum,25,50,75 assume mimimmum means 0,maximum means 100 then
1)mean=0+25+50+75+100/5=170 the mean value is 170
2)median 25+75+50/3 The median is the midpoint of a distribution
then we will get 116.66
the median value is 116.6
3)The mode is the most frequently occurring value there is frequntly occuring values so mode is 0
4) The trimean is a weighted average of the 25th percentile, the 50th percentile, and the 75th percentile. Letting P25 be the 25th percentile, P50 be the 50th and P75 be the 75th percentile, the formula for the trimean is:
Trimean = (P25 + 2P50 + P75)/4
from the formula, the median is weighted twice as much as the 25th and 75th percentiles.
5) The geometric mean is computed by multiplying all the numbers together and then taking the nth root of the product. For example, for the numbers 1, 10, and 100, the product of all the numbers is: 1 x 10 x 100 = 1,000. Since there are three numbers, we take the cubed root of the product (1,000) which is equal to 10. The formula for the geometric mean is therefore
so 0*25*50*75*100=0
5) The range is the simplest measure of variability to calculate, and one you have probably encountered many times in your life. The range is simply the highest score minus the lowest score
100-0=100
range =100
6)interquartile range
The interquartile range (IQR) is the range of the middle 50% of the scores in a distribution. It is computed as follows:
IQR = 75th percentile - 25th percentile
75-25=50
interquartile range is 50
6)variance
Variability can also be defined in terms of how close the scores in the distribution are to the middle of the distribution. Using the mean as the measure of the middle of the distribution, the variance is defined as the average squared difference of the scores from the mean.
If the variance in a sample is used to estimate the variance in a population, then the previous formula underestimates the variance and the following formula should be used: M=0+25+50+75+100/5=170
s^2=[170^2+(170-25)^2 +(170-75)^2 +(170-50)^2 + (170-100)^2]/(5-1)
=28900+21025+9025+1440+4900/4
43575
8) standard deviation
The standard deviation is simply the square root of the variancc
208.74625745
---2---
Central tendency: median
Variability : Range
---3---
Range and inter quartile range
Range = max - min
Interquartile range is Q3 - Q1
Median is Q2
---4---
median- 50th percentile
tri-mean- it is defines as (Q1+2MD+Q3)/4
Range-minimum-maximum
interquartile range-IQR=Q3-Q1
Note: On the 4th answer, what is MD when defining tri-mean?
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General guidance
Concepts and reason
Statistical constants which enable us to comprehend in a single effort the significance of the whole is known as measures of central tendency. A measure of central tendency gives us an idea about the concentration of the values in the central part of the distribution. It is value of the variable which is representative of the entire distribution.
Dispersion is the measure of extent to which individual items vary.
The word dispersion means scatteredness. Measures of variability tell the spread of the frequency distribution how widely the observations spread out around the measure of central tendency.
Fundamentals
The mean of the sample is calculated by using the following formula:
\bar x = \frac{{\sum\limits_{i = 1}^n {{x_i}} }}{n}xˉ=ni=1∑nxi
The geometric mean is calculated by using the following formula:
GM = {\left( {{x_1} \times {x_2} \times \cdots \times {x_n}} \right)^{1/n}}GM=(x1×x2×⋯×xn)1/n
The trimmed mean is calculated by using the following formula:
Tri - mean = \frac{{{Q_1} + 2{Q_2} + {Q_3}}}{4}Tri−mean=4Q1+2Q2+Q3
Mode is the most frequently occurred observation in the given data set.
Median is calculated by using the middle most values. It is equal to the 50th percentile.
Range for the given data is calculated by using the following formula:
R = {\rm{Maximum value}} - {\rm{Minimum value}}R=Maximumvalue−Minimumvalue
Interquartile range is calculated by using the following formula:
IQR = {Q_3} - {Q_1}IQR=Q3−Q1
The variance is calculated by using the following formula:
{\sigma ^2} = \frac{1}{n}\sum\limits_{i = 1}^n {{{\left( {{x_i} - \bar x} \right)}^2}}σ2=n1i=1∑n(xi−xˉ)2
The Standard deviation is calculated by using the following formula:
\sigma = \sqrt {\frac{1}{n}\sum\limits_{i = 1}^n {{{\left( {{x_i} - \bar x} \right)}^2}} }σ=n1i=1∑n(xi−xˉ)2
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FIRST STEP | ALL STEPS | ANSWER ONLY
Step-by-step
Step 1 of 2
The median of a set of data is the value which divides the data in two equal halves i.e. half of the values are greater than the median and the rest are lesser.
Trimmed mean is the mean of the numbers after eliminating the smallest and largest numbers form the arranged data.
The simplest measure of variation is the range. The Range is a measure of variation that is computed by finding the difference between the maximum and minimum values in a data set.
Interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. The interquartile range is the difference between the upper and lower quartile.
Quartiles divide a rank-ordered data set into four equal parts.
Explanation | Hint for next step
According to the properties of measures of central tendency and measures of dispersion If the minimum, the maximum and 25th, 50th, and 75th percentile of a distribution is known then mean, mode, variance, standard deviation, geometric mean cannot be calculated. Since, most of these measures are based upon all the observations.
Step 2 of 2
From the given information,
25th percentile is also known as first quartile.
50th percentile is also known as second quartile.
75th percentile is also known as third quartile.
Median is nothing but 50th percentile.
Tri-mean is calculated by using the three quartiles.
Tri - mean = \frac{{{Q_1} + 2{Q_2} + {Q_3}}}{4}Tri−mean=4Q1+2Q2+Q3
Range depends only on the extreme values.
Range = {\rm{Maximum - Minimum}}Range=Maximum−Minimum
The inter-quartile range is calculated by using third and first quartiles.
IQR = {Q_3} - {Q_1}IQR=Q3−Q1
If the minimum, the maximum and 25th, 50th, and 75th percentile of a distribution is known then the following measures can be found.
1.Median
2.Tri-mean
3.Range
4.Interquartile range
Explanation
Following are the some of the measures of central tendency or variability that are determined if the minimum, maximum, 25th, 50th, and 75th percentile of a distribution is known.
They are,
1.Median
2.Tri-mean
3.Range
4.Interquartile range
Answer
If the minimum, the maximum and 25th, 50th, and 75th percentile of a distribution is known then the following measures can be found.
1.Median
2.Tri-mean
3.Range
4.Interquartile range
