Measures of Central Tendency Summative Task Criterion: Investigating Patterns

On a separate paper hand out the solution of the two parts of the investigation.

Part One -

Use the given data set to solve the following problems:

50, 55, 60, 60, 70, 80

A. Find the mean, median, and mode of the given Data set.

B. Suppose that we increase each value by 4, recalculate the measures of the centre.

(Represent the new measures of the central tendency and the original one in a table)

C. What effect does increasing each value on each measure of central tendency?

D. Suppose that we decrease each value by 4, recalculate the measures of the centre.

(Represent the new measures of the central tendency and the original one in a table)

E. What effect does decreasing each value on each measure of central tendency?

F. Suppose that we multiply each value by x,   where x ∈ R, recalculate the measures of the center.

(Represent the new measures of the central tendency and the original one in a table)

G. What effect does multiplying each value on each measure of central tendency?

H. Suppose that we divide each value by x, where x ∈ R, recalculate the measures of the centre.

(Represent the new measures of the central tendency and the original one in a table)

I. What effect does dividing each value on each measure of central tendency?

J. If the set of data x₁, x₂, x₃, x₄, ... ,x_n is changed according to the linear relationship y_m = ax + b, a, b ∈  R where x: is the variable before changing

             y: is the variable after changing

Describe the ruleof each of the measures of central tendency for this set of data (y₁, y₂, y₃, ......... y_m).

(Interpret your conclusion using mathematical language)

Prove and justify the general rule for each measures of central tendency. (Prove: Use a sequence of logical steps to obtain the result in formal way)

Part Two -

Use the given data set to solve the following problems:

10, 20, 18, 8, 13, 15, 11, 58, 8

A. Find the mean, median, and mode of the given data set.

B. What effect does removing the outlier have on each of the measures of central tendency? Justify your answer.

i. Mean

ii. Mode

iii. Median

Use the given data set to solve the following problems:

40.5, 3.75, 4.75, 4.75, 3.75, 5.5, 6.5

 A. Find the mean, median, and mode of the given data set.

B. What effect does removing the outlier have on each of the measures of central tendency? Justify your answer. (Justify: Give valid reasons or evidence to support an answer or conclusion)

i. Mean

ii. Mode

 iii. Median

Use the given data set to solve the following problems:

2, 54, 57, 44, 54, 69, 71, 73, 74, 62

A. Find the mean, median, and mode of the given data set.

B. What effect does removing the outlier have on each of the measures of central tendency? Justify your answer.

i. Mean

ii. Mode

 iii. Median

How does removing the outliers affect the measures of central tendency? Justify your answer.