Question 1 - Arizona State University



Chapter 3. Statistics

This lecture note is based on the text book Mathematical Literacy in a numerate Society – by Matthew A. Isom and Jay Abramson

What is meant by causation and correlation? Read from your text page # 85.

Scatter Plot: A scatter plot is a graph of ordered pairs that allows us to examine the relation between two sets of data.

Example 1: a) Use calculator (or by hand) to make a scatter plot of the following data sets:

|Placement score |70 |68 |56 |40 |78 |59 |

|Beneficiary |Education |Cities |Highways |S. Citizens |Libraries |Other |

Make the table of proceeds as a percent and find interior angle for each sector. The Pie chart looks like the one below.

[pic]

Measure of Central Tendency: Mean Median and Mode:

Example 3: Calculate mean, median and mode.

a) 12, 39, 42, 11, 23, 41, 32, 44, 33, 31, 29, 37, 19, 25, 23, 18, 21, 13, 25, 23

b) [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic]

c) [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic]

Standard Deviation: The standard deviation is a measure of how widely values are dispersed from the mean.

We calculate the sample standard deviation by the following formula [pic], the notation [pic] has the name sigma and n is the total number of data points.

Example 4: Calculate mean and standard deviation.

a) 12, 39, 42, 11, 23, 41, 32, 44, 33, 31

b) [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic]

c) [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic], [pic]

Normal Distribution and the z – score: A normal distribution for a data set means that there are more data points close to the average and less data farther from the average until finally relatively few data points tend to one extreme or the other. Quite often we draw the normally distributed bell shaped curve free hand. We calculate z – score by the formula z – score = [pic]. The table value of z – score can be found at page # 110 in your text book. The table value of z – score for a certain data point indicates the area under the normal curve and between the data point and the mean.

Example 5. Given the mean value is 78, with standard deviation 13. Find the z – score for the data point 82.16 and the table value. Draw a normal curve and show the area enclosed by your data value and mean under the normal curve.

The z – score is 0.32, the table value for this z – score is 0.1255 = 12.55%.

GOOD LUCK

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Other

Libraries

Education

S. Citizens

Highways

Cities

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