Question

I did not post the data first because it is to long , thank you for your interest in my question I post the data

Agricultural data from the 2010 Census has been summarized for counties in Illinois. Use Explorat Data Analysis techniques for the following variables: NUM FARMS, AVG SIZE, CROP ACR Corn Yield, SoyYield, and WheatYield. Be sure to comment on all results. (a) Fill in the correct statistics for each of these variables in the following table: Standard Deviation Maximum Mean VariableMinimumMedian NUM FARMS AVG SIZE CROP ACR CornYield SoyYield WheatYield (b) Provide histograms and boxplots for each of these variables and comment on each. (c) Provide a summary in the context of this scenario.

Actually I solve this questions but I have question about the comment on each histogram and box plots that I got . what can I say for each one can someone explain that to me and give me idea about it and show me in any example for histogram and box posts what can I write ?

I

Answer 1

Below i give an examples about interpretation of box plot and histogram.

it is very useful for u.thank you

One of the features that a histogram can show you is the shape of the statistical data — in other words, the manner in which the data fall into groups. For example, all the data may be exactly the same, in which case the histogram is just one tall bar; or the data might have an equal number in each group, in which case the shape is flat.

Some data sets have a distinct shape. Here are three shapes that stand out:

• Symmetric. A histogram is symmetric if you cut it down the middle and the left-hand and right-hand sides resemble mirror images of each other:

• 

  Time Spent Filling Out a Survey (n:50) a 20 15 8 10 1.5 2.5 3.5 4.5 5.5 Time (minutes)

• The above graph shows a symmetric data set; it represents the amount of time each of 50 survey participants took to fill out a certain survey. You see that the histogram is close to symmetric.

• Skewed right. A skewed right histogram looks like a lopsided mound, with a tail going off to the right:

• 

This graph, which shows the ages of the Best Actress Academy Award winners, is skewed right. You see on the right side there are a few actresses whose ages are older than the rest. Most of the actresses were between 20 and 50 years of age when they won. A few actresses were between 60–65 years of age when they won their Oscars, and a handful were 70 years or older. The last three bars are what make the data have a shape that is skewed right.

Skewed left. If a histogram is skewed left, it looks like a lopsided mound with a tail going off to the left:

This graph shows a histogram of 17 exam scores. The shape is skewed left; you see a few students who scored lower than everyone else.

Don’t expect symmetric data to have an exact and perfect shape. Data hardly ever fall into perfect patterns, so you have to decide whether the data shape is close enough to be called symmetric.

If the differences aren’t significant enough, you can classify it as symmetric or roughly symmetric. Otherwise, you classify the data as non-symmetric.

Don’t assume that data are skewed if the shape is non-symmetric. Data sets come in all shapes and sizes, and many of them don’t have a distinct shape at all. Skewness is mentioned here because it’s one of the more common non-symmetric shapes, and it’s one of the shapes included in a standard introductory statistics course.

If a data set does turn out to be skewed (or close to it), make sure to denote the direction of the skewness (left or right).

How to read a box plot/Introduction to box plots

Box plots are drawn for groups of W@S scale scores. They enable us to study the distributional characteristics of a group of scores as well as the level of the scores.

To begin with, scores are sorted. Then four equal sized groups are made from the ordered scores. That is, 25% of all scores are placed in each group. The lines dividing the groups are called quartiles, and the groups are referred to as quartile groups. Usually we label these groups 1 to 4 starting at the bottom.

Definitions

Median
The median (middle quartile) marks the mid-point of the data and is shown by the line that divides the box into two parts. Half the scores are greater than or equal to this value and half are less.

Inter-quartile range
The middle “box” represents the middle 50% of scores for the group. The range of scores from lower to upper quartile is referred to as the inter-quartile range. The middle 50% of scores fall within the inter-quartile range.

Upper quartile
Seventy-five percent of the scores fall below the upper quartile.

Lower quartile
Twenty-five percent of scores fall below the lower quartile.

Whiskers
The upper and lower whiskers represent scores outside the middle 50%. Whiskers often (but not always) stretch over a wider range of scores than the middle quartile groups.

Interpreting box plots/Box plots in general

Box plots are used to show overall patterns of response for a group. They provide a useful way to visualise the range and other characteristics of responses for a large group.

The diagram below shows a variety of different box plot shapes and positions.

Some general observations about box plots

The box plot is comparatively short – see example (2). This suggests that overall students have a high level of agreement with each other.

The box plot is comparatively tall – see examples (1) and (3). This suggests students hold quite different opinions about this aspect or sub-aspect.

One box plot is much higher or lower than another – compare (3) and (4) – This could suggest a difference between groups. For example, the box plot for boys may be lower or higher than the equivalent plot for girls. Follow this up by looking at the Items at a Glance reports.

Obvious differences between box plots – see examples (1) and (2), (1) and (3), or (2) and (4). Any obvious difference between box plots for comparative groups is worthy of further investigation in the Items at a Glancereports.

Your school box plot is much higher or lower than the national reference group box plot. This also suggests an area of difference that could be explored further in the Items in Detail reports and through consultation.

The 4 sections of the box plot are uneven in size – See example (1). This shows that many students have similar views at certain parts of the scale, but in other parts of the scale students are more variable in their views. The long upper whisker in the example means that students views are varied amongst the most positive quartile group, and very similar for the least positive quartile group. The Items in Detail reports can be used to explore this further.

Same median, different distribution – See examples (1), (2), and (3). The medians (which generally will be close to the average) are all at the same level. However the box plots in these examples show very different distributions of views.
It always important to consider the pattern of the whole distribution of responses in a box plot.