Question

 

1.What happens to the mean or median when each number in a set of data is multiplied by a constant?

2.Predict how measures of spread are affected by new or altered individual entries in a dataset. That is, a small number is replaced by a very big number, for example.

3.What is the relationship between the standard deviation and the variance? What characteristic of a set of data causes a large standard deviation? A small one?

4.What procedure did you use to determine whether a distribution is Normal? What are the characteristics of a normal distribution? How does the distribution shape change as the standard deviation gets bigger? smaller?

5.Give two examples of each of the following: categorical (qualitative) and quantitative variables; discrete and continuous variables.

6.Are bar graphs, pie charts, dot plots, stem and leaf plots and histogram qualitative or quantitative data?

Answer 1

1.What happens to the mean or median when each number in a set of data is multiplied by a constant?

Mean =

Median = Middle-most element

If all data are multiplied by a constant c, then,

New Mean =

New Median = c * Middle-most element = c * (old median)

Thus, mean and median are multiplied by the constant.

2.Predict how measures of spread are affected by new or altered individual entries in a dataset. That is, a small number is replaced by a very big number, for example.

If a small number is replaced by a very big number, then the measures of spread will increase. If a big number is increased by a number close to the mean, then the  measures of spread will decrease.

3.What is the relationship between the standard deviation and the variance? What characteristic of a set of data causes a large standard deviation? A small one?

variance = (standard deviation)²

The data with large range and widely spread causes a large standard deviation. The data with small range and narrowly spread causes a small standard deviation.

4.What procedure did you use to determine whether a distribution is Normal? What are the characteristics of a normal distribution? How does the distribution shape change as the standard deviation gets bigger? smaller?

Ch-square test for goodness of fit or plotting a q-q plot can be used to determine whether a distribution is Normal. Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal. A normal distribution is perfectly symmetrical around its center. When the standard deviation gets bigger, the bell shape will become more flat and wider. When the standard deviation gets smaller, the bell shape will be narrower and have sharp peak.

5.Give two examples of each of the following: categorical (qualitative) and quantitative variables; discrete and continuous variables.

categorical (qualitative) - Sex (male/Female), Ice-cream Flavor(Chocolate, Vanilla, Strawberry(

quantitative variables - Age, Height

discrete - Number of customers in the shop, Number of dice rolls till we get 6

continuous variables - Age, Height

6.Are bar graphs, pie charts, dot plots, stem and leaf plots and histogram qualitative or quantitative data?

For qualitative data, we can use bar or pie charts.
For quantitative date, we can use dot plots, stem and leaf plots and histogram.