How does Standard Deviation affect normal curve?
Know that changing the mean of a normal density curve shifts the curve along the horizontal axis without changing its shape. Know that increasing the standard deviation produces a flatter and wider bell-shaped curve and that decreasing the standard deviation produces a taller and narrower curve.
Which curve has a smaller standard deviation?
The curve with a higher peak has a smaller standard deviation; the data values with a resulting histogram that gives rise to the taller and narrower normal curve are less spread out along the horizontal axis than those values leading to the shorter curve.
Which curve has the larger standard deviation?
What does a narrow bell curve mean?
A bell curve graph depends on two factors: the mean and the standard deviation. ... For example, a large standard deviation creates a bell that is short and wide while a small standard deviation creates a tall and narrow curve.
Are bimodal distributions normal?
Data distributions in statistics can have one peak, or they can have several peaks. The type of distribution you might be familiar with seeing is the normal distribution, or bell curve, which has one peak. The bimodal distribution has two peaks.
How do you know if a distribution is bimodal?
A mixture of two normal distributions with equal standard deviations is bimodal only if their means differ by at least twice the common standard deviation. Estimates of the parameters is simplified if the variances can be assumed to be equal (the homoscedastic case).
Are bimodal distributions symmetric?
The normal distribution is symmetric. ... Distributions don't have to be unimodal to be symmetric. They can be bimodal (two peaks) or multimodal (many peaks). The following bimodal distribution is symmetric, as the two halves are mirror images of each other.
Are bimodal distributions skewed?
How would you describe the shape of the histogram? Bell-shaped: A bell-shaped picture, shown below, usuallypresents a normal distribution. Bimodal: A bimodal shape, shown below, has two peaks. ... Skewed left: Some histograms will show a skewed distribution to the left, as shown below.
How do you tell if a distribution is unimodal or bimodal?
A histogram is unimodal if there is one hump, bimodal if there are two humps and multimodal if there are many humps. A nonsymmetric histogram is called skewed if it is not symmetric. If the upper tail is longer than the lower tail then it is positively skewed.
What does a left skewed histogram mean?
A symmetric distribution is one in which the 2 "halves" of the histogram appear as mirror-images of one another. ... A "skewed left" distribution is one in which the tail is on the left side. The above histogram is for a distribution that is skewed right.
How do you tell if a histogram is unimodal or bimodal?
A unimodal distribution only has one peak in the distribution, a bimodal distribution has two peaks, and a multimodal distribution has three or more peaks. Another way to describe the shape of histograms is by describing whether the data is skewed or symmetric.
What is unimodal bimodal Trimodal Polymodal?
The mode of a set of observations is the most commonly occurring value. ... A distribution with a single mode is said to be unimodal. A distribution with more than one mode is said to be bimodal, trimodal, etc., or in general, multimodal. The mode of a set of data is implemented in the Wolfram Language as Commonest[data].
What is bimodal example?
Bimodal literally means "two modes" and is typically used to describe distributions of values that have two centers. For example, the distribution of heights in a sample of adults might have two peaks, one for women and one for men.
How are a Stemplot and a histogram similar?
A stem and leaf plot is a way to plot data where the data is split into stems (the largest digit) and leaves (the smallest digits). ... The stem and leaf plot is used like a histogram; it allows you to compare data. While a histogram uses bars to represent amounts, the leaves of the stemplot represent amounts.
What is the difference between box plot and histogram?
Histograms and box plots are graphical representations for the frequency of numeric data values. ... Histograms are preferred to determine the underlying probability distribution of a data. Box plots on the other hand are more useful when comparing between several data sets.
What does a histogram show that a Boxplot does not?
In the univariate case, box-plots do provide some information that the histogram does not (at least, not explicitly). That is, it typically provides the median, 25th and 75th percentile, min/max that is not an outlier and explicitly separates the points that are considered outliers.
How do you read a Stemplot?
This stemplot is read as follows: the stem is the tens digit and each digit in the "leaves" section is a ones digit. Put them together to have a data point. In the particular case there are 15 data points therefore the median is 79. Thus the first quartile is 69 and the third quartile is 87.
What is the center of a Stemplot?
The center of a distribution is the middle of a distribution. For example, the center of 1 2 3 4 5 is the number 3. ... Look at a graph, or a list of the numbers, and see if the center is obvious. Find the mean, the “average” of the data set. Find the median, the middle number.
How do you describe a Stemplot?
A stem and leaf plot looks something like a bar graph. Each number in the data is broken down into a stem and a leaf, thus the name. The stem of the number includes all but the last digit. The leaf of the number will always be a single digit.
Is standard deviation a measure of spread?
The variance and the standard deviation are measures of the spread of the data around the mean. They summarise how close each observed data value is to the mean value. ... The standard deviation of a normal distribution enables us to calculate confidence intervals.
How do you find the spread?
There are three methods you can use to find the spread in a data set: range, interquartile range, and variance. Range is the difference between the highest and lowest values in a data set. You can find the range by taking the smallest number in the data set and the largest number in the data set and subtracting them.
Which measure of spread is best for skewed data?
When it is skewed right or left with high or low outliers then the median is better to use to find the center. The best measure of spread when the median is the center is the IQR. As for when the center is the mean, then standard deviation should be used since it measure the distance between a data point and the mean.
How do you determine which measure of center best represents the data?
Mean is the most frequently used measure of central tendency and generally considered the best measure of it. However, there are some situations where either median or mode are preferred. Median is the preferred measure of central tendency when: There are a few extreme scores in the distribution of the data.
What are the most appropriate measures of center and spread for this data set?
When the mean is the most appropriate measure of center, then the most appropriate measure of spread is the standard deviation. This measurement is obtained by taking the square root of the variance -- which is essentially the average squared distance between population values (or sample values) and the mean.
What does the Iqr tell you about the data?
The IQR tells how spread out the "middle" values are; it can also be used to tell when some of the other values are "too far" from the central value. These "too far away" points are called "outliers", because they "lie outside" the range in which we expect them.
What if the IQR is zero?
The IQR is a measure of variability and the mean is a measure of central tendency. ... Having an IQR of 0 means there is no variability in the middle 50% of your data, but the center of the distribution can be anywhere.
What is the 1.5 IQR rule?
What does the standard deviation represent?
What is standard deviation? Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.
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