# Relationship between box plots and histograms skewed

### Interpreting a box plots shape

Since histogram area is proportional to relative frequency, the median and quartiles The diagram below shows the box plot of a symmetric distribution under the and quartile on the other side, this shows that the distribution is skew . Two common graphical representation mediums include histograms and box plots, also called The only difference between a histogram and a bar chart is that a histogram displays This may lead one to assume the data is slightly skewed. The Box Plot, sometimes also called "box and whiskers plot", combines the if we were to draw a histogram for this data it would look slightly skewed to the or skewed to the right, and estimate the value of the mean in relation to the median.

What does a box plot tell you about the distribution? Centre The vertical line inside the box the median gives an indication of the centre of the distribution.

## Comparing Box Plots and Histograms – Which Is the Better Tool?

Spread The width of the box the interquartile range gives an indication of the spread of values in the distribution. Shape High density corresponds to adjacent box plot values being close together. In particular, if the extreme and quartile on one side are closer to the median than the extreme and quartile on the other side, this shows that the distribution is skew.

The diagram below shows the jittered dot plot and box plot of a batch of values.

## Comparing dot plots, histograms, and box plots

Use the Centre slider to observe how the box plot shows the 'centre' of the distribution of values. Use the Spread slider to observe how the box plot shows the spread of values in the data.

Return the Spread slider to its maximum, then investigate the effect of the Skewness slider. For example, a high density to the left of the distribution and a long tail to the right results in the lower extreme and quartile being close to the median.

What Is a Histogram? A histogram is a type of bar chart that graphically displays the frequencies of a data set.

### Comparing dot plots, histograms, and box plots (video) | Khan Academy

Similar to a bar chart, a histogram plots the frequency, or raw count, on the Y-axis vertical and the variable being measured on the X-axis horizontal. The only difference between a histogram and a bar chart is that a histogram displays frequencies for a group of data, rather than an individual data point; therefore, no spaces are present between the bars.

Typically, a histogram groups data into small chunks four to eight values per bar on the horizontal axisunless the range of data is so great that it easier to identify general distribution trends with larger groupings.

What Is a Box Plot? A box plot, also called a box-and-whisker plotis a chart that graphically represents the five most important descriptive values for a data set. These values include the minimum value, the first quartile, the median, the third quartile, and the maximum value.

**Thinking about shapes of distributions - Data and statistics - 6th grade - Khan Academy**

When graphing this five-number summary, only the horizontal axis displays values. Within the quadrant, a vertical line is placed above each of the summary numbers. Comparing Histograms and Box Plots Although histograms and box plots are collectively part of the chart aid category, they do represent very different types of charts. Both charts effectively represent different data sets; however, in certain situations, one chart may be superior to the other in achieving the goal of identifying variances among data.