Read Summary Below and answer QUESTION 1

Z score: a measure of how many standard deviations you are away from the norm (average or mean)

Please make sure that you understand this concept.

A Z-score is a method used to convert a raw score (data value = x) into units of the normal curve (z distribution) called standard deviation (SD) groups. When comparing z-scores, you are using a method of graphically illustrating individual's obtained z-scores against the sample mean z-scores for any given variable

"Is my z-score better than yours? If so, what does that mean?"

Here is the formula:

Formulaforasamplez=(xmeans)

Formulaforapopulationz=(x)

Round the z scores to two decimal places (100th) Example: 2.31

Essential properties of a z score are the number of standard deviations that a given value (x) is above or below the mean (z is 0 at the mean). A z score is expressed as a number with no units of measurement. A data value is significantly low if its z score is less than or equal to -2, or the value is significantly high if its z score is greater than or equal to +2.

*Remember that values more than two standard deviations away from the mean are considered significant.*

If an individual data value is less than the mean, its corresponding z score is a negative number.

Example: Comparing Baby's Weight and Adult Body Temperature

Which of the following two data values is more extreme relative to the data set from which it came?

• The 4,000g weight of a newborn baby (among 400 weights with sample mean 3152.0g and a sample standard deviation 693.4g)
• The 99^oF temperature of an adult (among 106 adults with sample mean 98.20⁰F and sample standard deviation 0.62⁰F)

Solution

The 4000g weight and the 99⁰F body temperature can be standardized by converting each of them to z scores.

4000g birth weight:

z=xmeans=4000g3152.0g693.4g=1.22

99⁰F body temperature:

z=xmeans=990F398.200F0.620F=1.29

Remember that z scores do not have units.

What is observed is that the z score of the body temperature (1.29) is higher than the z score (1.22) of the birth weight. This is how it is interpreted.

The z scores show that the 4000g birth weight is 1.22 standard deviations above the mean, and the 99⁰F body temperature is 1.29 standard deviations above the mean. Because the body temperature is farther above the mean, it is the more extreme value. A 99⁰F body temperature is slightly more extreme than a birth weight of 4000g.

*****We use z scores to identify significant values. Significant values are those with

zscores2.00or2.00.

******Not Significant Values are those with

zscores2.00and2.00.

QUESTION #1

Is a platelet count of 75 significantly low? We need to know if the patient "A" has cancer. Thrombocytopenia is a condition in which you have alowbloodplatelet count.Platelets(thrombocytes) are colorless blood cells that help blood clot.Platelets stop bleeding by clumping and forming plugs in blood vessel injuries. Alow platelet countis a blood disorder that has a long list of possiblecauses. The condition affects the ability of the blood to clot, and wounds can bleed severely with this condition. This can haveseverecomplications in some cases.

Show your calculations on paper and upload a picture of it into canvas as an attachment. Explain your answer in Canvas under the submission box. Your mathematical diagnosis will have serious ramifications.

The lowest platelet count in a dataset is 75. Is that value significantly low? Assume that platelet counts have a mean of 239.4 and a standard deviation of s=64.2.