What kind of data is represented in a histogram

Video transcript Let's say you have a cherry pie store. Some pies might have over cherries, while other pies might have fewer than 50 cherries. So what you're curious about is what is the distribution, how many of different types of pies do you have? So, to do that, you set up a histogram. You take each pie in your store, and you count the number of cherries on it. This pie has 1,2,3,4,5 6,7,8,9,10,keep counting Let's say it has 32 cherries.

And you are going to do it for every pie. The heights of rectangles are proportional to corresponding frequencies of similar as well as for different classes. Let's learn about histograms more in detail. A histogram is the graphical representation of data where data is grouped into continuous number ranges and each range corresponds to a vertical bar.

A histogram graph is a bar graph representation of data. It is a representation of a range of outcomes into columns formation along the x-axis. It is the easiest manner that can be used to visualize data distributions.

Let us understand the histogram graph by plotting one for the given below example. Uncle Bruno owns a garden with 30 black cherry trees. Each tree is of a different height. The height of the trees in inches : 61, 63, 64, 66, 68, 69, 71, We can group the data as follows in a frequency distribution table by setting a range:.

This data can be now shown using a histogram. Example: Construct a histogram for the following frequency distribution table that describes the frequencies of weights of 25 students in a class.

A frequency histogram is a histogram that shows the frequencies the number of occurrences of the given data items. For example, in a hospital, there are 20 newborn babies whose ages in increasing order are as follows: 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5.

This information can be shown in a frequency distribution table as follows:. The histogram can be classified into different types based on the frequency distribution of the data. There are different types of distributions, such as normal distribution, skewed distribution, bimodal distribution, multimodal distribution, comb distribution, edge peak distribution, dog food distribution, heart cut distribution, and so on.

The histogram can be used to represent these different types of distributions. We have mainly 5 types of histogram shapes. They are listed below:. Let us discuss the above-mentioned types of histogram or histogram shapes in detail with the help of practical illustrations. A bell-shaped histogram has a single peak. The histogram has just one peak at this time interval and hence it is a bell-shaped histogram.

For example , the following histogram shows the number of children visiting a park at different time intervals. This histogram has only one peak. The categories of a histogram are usually specified as consecutive, non-overlapping intervals of a variable. The categories intervals must be adjacent and often are chosen to be of the same size.

The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous. In statistical terms, the frequency of an event is the number of times the event occurred in an experiment or study. The relative frequency or empirical probability of an event refers to the absolute frequency normalized by the total number of events:. Put more simply, the relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample.

The height of a rectangle in a histogram is equal to the frequency density of the interval, i. A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the total area equaling one. As mentioned, a histogram is an estimate of the probability distribution of a continuous variable.

To define probability distributions for the simplest cases, one needs to distinguish between discrete and continuous random variables. In the discrete case, one can easily assign a probability to each possible value.

In contrast, when a random variable takes values from a continuum, probabilities are nonzero only if they refer to finite intervals. Intuitively, a continuous random variable is the one which can take a continuous range of values — as opposed to a discrete distribution, where the set of possible values for the random variable is, at most, countable. There are many examples of continuous probability distributions: normal, uniform, chi-squared, and others.

The Histogram : This is an example of a histogram, depicting graphically the distribution of heights for 31 Black Cherry trees. Density estimation is the construction of an estimate based on observed data of an unobservable, underlying probability density function.

Histograms are used to plot the density of data, and are often a useful tool for density estimation. The unobservable density function is thought of as the density according to which a large population is distributed. The data are usually thought of as a random sample from that population. A probability density function, or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

Boxplot Versus Probability Density Function : This image shows a boxplot and probability density function of a normal distribution.

The above image depicts a probability density function graph against a box plot. A box plot is a convenient way of graphically depicting groups of numerical data through their quartiles. The spacings between the different parts of the box help indicate the degree of dispersion spread and skewness in the data and to identify outliers. In addition to the points themselves, box plots allow one to visually estimate the interquartile range.

A range of data clustering techniques are used as approaches to density estimation, with the most basic form being a rescaled histogram.

Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. To see this, we compare the construction of histogram and kernel density estimators using these 6 data points:. For the histogram, first the horizontal axis is divided into sub-intervals, or bins, which cover the range of the data.

In this case, we have 6 bins, each having a width of 2. If more than one data point falls inside the same bin, we stack the boxes on top of each other. Histogram Versus Kernel Density Estimation : Comparison of the histogram left and kernel density estimate right constructed using the same data.

The 6 individual kernels are the red dashed curves, the kernel density estimate the blue curves. The data points are the rug plot on the horizontal axis. For the kernel density estimate, we place a normal kernel with variance 2. The kernels are summed to make the kernel density estimate the solid blue curve.

Kernel density estimates converge faster to the true underlying density for continuous random variables thus accounting for their smoothness compared to the discreteness of the histogram. Distinguish between quantitative and categorical, continuous and discrete, and ordinal and nominal variables. A variable is any characteristic, number, or quantity that can be measured or counted.

A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables. Variables are so-named because their value may vary between data units in a population and may change in value over time. There are different ways variables can be described according to the ways they can be studied, measured, and presented.

Numeric variables may be further described as either continuous or discrete. A continuous variable is a numeric variable. Observations can take any value between a certain set of real numbers.

The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows. Examples of continuous variables include height, time, age, and temperature. A discrete variable is a numeric variable.

Observations can take a value based on a count from a set of distinct whole values. A discrete variable cannot take the value of a fraction between one value and the next closest value.

Examples of discrete variables include the number of registered cars, number of business locations, and number of children in a family, all of of which measured as whole units i. Therefore, categorical variables are qualitative variables and tend to be represented by a non-numeric value.

We and our partners process data to: Actively scan device characteristics for identification. I Accept Show Purposes. Your Money. Personal Finance. Your Practice. Popular Courses. What Is a Histogram? Key Takeaways A histogram is a bar graph-like representation of data that buckets a range of outcomes into columns along the x-axis. The y-axis represents the number count or percentage of occurrences in the data for each column and can be used to visualize data distributions.

In trading, the MACD histogram is used by technical analysts to indicate changes in momentum. Compare Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation. This compensation may impact how and where listings appear. Investopedia does not include all offers available in the marketplace. Related Terms Dot Plot A dot plot or dot chart consists of data points plotted on a graph. The Federal Reserve uses dot plots to show its predicted interest rate outlook.