What are they?
How do you construct one?
How can they be used to analyse data?

You may also include definitions, explanations, pictures, worked examples and diagrams with annotations.

A histogram is a display of bars using different widths and height. However, the bars have to be touching.

The area of the bar represents the frequency.

Her is a useful clip that teaches you about Histograms:

https://www.mathswatchvle.com/video/mwclip.php

So my fellow maths lovers , this is just how you do histograms :

You  measure the height of every  tree in the orchard in centimetres (cm)

The heights vary from 100 cm  to 340 cm

You decide to put the results into groups of 50 cm:

• The 100 to just below 150 cm range,
• The 150 to just below 200 cm range,
• etc...

Answer

• Class boundaries:
• The class boundaries are 0, 4, 11 and 19.
• (remember that this is age in years):

• Class widths:
• The class widths are therefore 4, 7 and 8.

Frequency densities:

¹²/₄ = 3

¹⁴/₇ = 2

⁴⁸/₈ = 6

The histogram should look like this:

To construct a histogram from a continuous variable you first need to split the
data into intervals, called bins. The ages have been split into bins, with each bin representing a 5-year period starting at 10 years. Each bin contains the number of occurrences of scores in the data set that are contained within that bin.

For an example:

You measure the height of every
tree in the orchard in centimetres (cm)
The heights vary from 100 cm to
340 cm
You decide to put the results
into groups of 50 cm:

• The 100 to just below 150 cm range,


• The 150 to just below 200 cm range,


• etc...

A histogram is a representation of data in the form of a bar chart. The diagram that consists of rectangles whose area is proportional to the frequency of the variables and the width is equal to the class interval.

How do you construct a histogram?

-To construct a you need to have a set of data this may be heights, weights, ages etc.

-Determine the minimum and maximum of the data you have recorded (aka the range)

-Construct the horizontal axis of the graph by recording the range of individual measurements, starting with the minimum recorded measurement and adding the individual measurements up to and including the maximum recorded measurement. Label this axis to designate the variables.

-Construct the vertical axis by recording the potential range of frequencies for each measurement. For most distributions, the expected range of the vertical axis would be from zero to a number equal to half  the total number of measurements.(e.g. if the total was 30 the vertical axis would have individual numbers from 0 to 15)

-Plot the individual data measurements on the graph by locating the data point on the horizontal axis and plotting an X on the graph for each occurrence. This will result in vertically stacked "X"s for multiple recordings of the same measurement.(e.g. 3 measurements of a test score of 70 would be stacked over the unit "70"  on the horizontal line and with the x opposite the 3 on the vertical axis)

- Continue plotting individual measurements until all have been plotted. The results of the completed chart will indicate the pattern of distribution for the measured data.

When are they used?

Histograms illustrate the process distribution and are used to make predictions about a stable process. If the system is unstable, the histogram will have little predictive value.

A histogram  is a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies."

Sounds complicated . . . but the concept really is pretty simple. We graph groups of numbers according to how often they appear. Thus if we have the set 1,2,2,3,3,3,3,4,4,5,6, we can graph them like this:

This graph is pretty easy to make and gives us some useful data about the set. For example, the graph peaks at 3, which is also the median and the mode of the set. The mean of the set is 3.27—also not far from the peak. The shape of the graph gives us an idea of how the numbers in the set are distributed about the mean: the distribution of this graph is wide compared to size of the peak, indicating that values in the set are only loosely bunched round the mean.

A histogram is a display of data using bars of different heights.

The area of a histogram represents the frequency.

There are no gaps in the columns of a histogram.

How to construct a histogram:

1. On the vertical axis, place frequencies. Label this axis "Frequency".
2. On the horizontal axis, place the lower value of each interval. ...
3. Draw a bar extending from the lower value of each interval to the lower value of the next interval.

Answer

• Class boundaries:
• The class boundaries are 0, 4, 11 and 19.
• (remember that this is age in years):

• Class widths:
• The class widths are therefore 4, 7 and 8.

Frequency densities:

¹²/₄ = 3

¹⁴/₇ = 2

⁴⁸/₈ = 6

The histogram should look like this:

The following table shows the ages of 25 children on a school bus:

If we are going to draw a histogram to represent the data, we first need to find the class boundaries. In this case they are 5, 11, 16 and 18. The class widths are therefore 6, 5 and 2.

The area of a histogram represents the frequency not the height.

The areas of our bars should therefore be 6, 15 and 4.

Remember that in a bar chart the height of the bar represents the frequency. It is therefore correct to label the vertical axis 'frequency'.

However, as in a histogram, it is the area which represents the frequency.

It would therefore be incorrect to label the vertical axis 'frequency' and the label should be 'frequency density'.

So we know that Area = frequency = Frequency density x class width hence:

Frequency density = frequency ÷ class width

Here is an example of a histogram; from this we can work out the frequency.

The class boundaries are 5-10, 11- 15, 16-17 and >17.

Using the class boundaries we can now work out the frequency. The first bar is 6 in width and 1 in height, therefore the frequency is 6 because 6 (width) x 1 (height) = 6.

To find the frequency of the yellow bar, we would have to multiply 5x3 because the width of the bar is 5 across and the height is 3 up.

https://www.tes.co.uk/teaching-resource/gcse-histograms-worksheet-6109880

Shoutout to my homie RONNY ATHO!!!!!

H-I - S-T-O-G   - R-A-M

Spells  histogram, histogram.

It’s  a way to visualize the data, data.

It’s  a way to use your calculator, -lator.

H-I - S-T-O-G   - R-A-M

You  see…

Put  your data in List one,

Press  Stat Plots to have some fun.

And  now, follow me.

H-I - S-T-O-G   - R-A-M

Spells  histogram, histogram.

Now  choose the final graphing application, -cation.

X  and Y will show your calculation, -lation.

H-I - S-T-O-G   - R-A-M

It’s  true…

Press  Zoom 9 to do the plot,

Then  press Trace to see what’s what.

And  you’re almost through.

H-I - S-T-O-G   - R-A-M

Spells  histogram, histogram.

It’s  time to write the final distribution, -bution.

Find  central trends with even less confusion, -fusion.

H-I - S-T-O-G   - R-A-M

You  see…

 WE HOPE THAT GIVES YOU A BIT OF JOY TO HISTOGRAMS

Just  press Stat and Calculate,

You’ll  see answers while you wait,

With  technology!

A histogram is a display of bars using different widths and height. However, the bars have to be touching.

The area of the bar represents the frequency.

Her is a useful clip that teaches you about Histograms:

https://www.mathswatchvle.com/video/mwclip.php