Q:
# Why are unequal class intervals sometimes used in a frequency distribution?

A:

**Unequal class intervals can be used in frequency distribution if the rate of occurrence is very unevenly distributed, with certain classes showing far lower or far greater frequencies than those on either side.** In many data tables and histograms, consistent intervals are used, but they cannot always account for irregularities and outliers like those that strategically use unequal intervals.

Wikipedia explains that frequency distribution is a representation of data in a grouped fashion that illustrates how often a particular interval is represented within a corresponding string of ungrouped data.

For example, the frequency distribution of times to finish a race might show the following:

40-50 seconds: 4 runners

50-60 seconds: 9 runners

60-70 seconds: 2 runners

Equal intervals work very well for tables that do not represent a large range or great amount of values. Math Is Fun shows that they can be easily converted into a histogram, which is like a bar graph but has connected bars that mark intervals instead of individual values.

However, with some larger sets of data, even intervals do not accurately reflect the findings in the experiment. For example, if all the students in a high school had their race times recorded, the distribution is extremely different. Clusters of students can form around the 1- and 2-minute marks, but there could be extreme outliers, such as those who decided to walk instead of run.

The data table can show the following:

0-60 seconds: 58

60-120 seconds: 462

120-180 seconds: 321

180-240 seconds: 72

240-300 seconds: 26

300-360 seconds: 61

However, because no one ran it in under 40 seconds and because there were no values represented between 3.5 and 4.5 minutes, the above frequency distribution is not very representative.

The following distribution in 20-second intervals presents a more accurate picture:

40-60 seconds: 58

60-80 seconds: 201

80-100 seconds: 179

100-120 seconds: 82

120-140 seconds: 185

140-160 seconds: 76

160-180 seconds: 60

180-200 seconds: 72

*200-280 seconds: 0

280-300 seconds: 26

300-320 seconds: 43

320-340 seconds: 18

Learn more in Statistics-
Q:
## What is a bimodal distribution?

A:

Full Answer >**A bimodal distribution is a chart of frequency that has two different peaks or modes.**The term mode here refers to a local high point of the chart and is not related to the other common usage of "mode," which refers to the most frequent number found in a distribution.Filed Under: -
Q:
## How do you calculate frequency?

A:To calculate wave frequency in physics, one must know about the variables used in different formulas. One formula states that frequency (f) is equal to the wave velocity (v) divided by the wavelength (λ), or f = v/ (λ). If you know the period (T), another formula you can use is that frequency is the reciprocal of the period, or f= 1/T.

Full Answer >Filed Under: -
Q:
## What is the CDF for the binomial distribution?

A:The cumulative distribution function for a binomial distribution is f(k; n, p) = (p^i)(1 - p)^(n - i) between the limits of i and k. K is defined as the total possible number of successful outcomes, p is the probability and n is the number of independent events.

Full Answer >Filed Under: -
Q:
## What is the variance of uniform distribution?

A:

Full Answer >**The variance is the second central moment of a continuous probability distribution.**The variance of a continuous uniform distribution on the interval [a, b] is (1/12)*(b - a)^2.Filed Under: