# Math Help - Graphing Questions

1. ## Graphing Questions

Hello everyone. These questions are from a grade 12 Data Management class. Any help would be appreciated. Thanks!

#1)Alice is constructing a histogram to display data with a range of 12. She decided on a bin width of 3. Explain why this is not a good choice.

#2) A Histogram is constructed for a set of data. How would the shape of the histogram change if each of the data was multiplied by the same negative number? In particular, describe the effect of this transformation for U-Shaped, uniform, mound-shaped, right-scewed and left scewed histograms.

2. Originally Posted by crazy_gal108
Hello everyone. These questions are from a grade 12 Data Management class. Any help would be appreciated. Thanks!

#1)Alice is constructing a histogram to display data with a range of 12. She decided on a bin width of 3. Explain why this is not a good choice.
I expect that the answer you are expected to give to this question is
that a bin width 0f 3 will give the data all falling within about 5 bins
which will be a bit to coarse to show whatever it is you expect the
histogram to show.

In the real world the number of bins you use depends on a number of factors.
The main one is "what do you want the histogram to show?" a second
important factor is "how many data points do you have?".

There are a number of formulas for the appropriate number of bins or bin
width to use for a histogram. Two of the most common are:

Scott's rule:

$
h\approx \frac{3.5 \times \sigma}{n^{1/3}}
$

where h is the recommended bin width, and $\sigma$ is an estimate
of the standard deviation of the data or underlying distribution, and $n$
is the number of data points.

Freedman & Diaconis's rule:

$
h\approx \frac{2 \times \mathrm{IQR}}{n^{1/3}}
$

where $\mathrm{IQR}$ is the interquartile range of the data.

RonL

3. Originally Posted by crazy_gal108

#2) A Histogram is constructed for a set of data. How would the shape of the histogram change if each of the data was multiplied by the same negative number? In particular, describe the effect of this transformation for U-Shaped, uniform, mound-shaped, right-scewed and left scewed histograms.
I think you should try this one yourself. Try making up some data, draw a
histogram, then multiply the data by say -3 and plot another histogram and
see what it looks like.

RonL