Question

model 2 - foot width in a high school classroom
female foot width (cm) male foot width (cm)
7.8 10
8 10.5
8 9
5 9.3
17 13
7.5 7.5
7.5 10
7 9.2
7.8 9
7 4.5

1. refer to the data in model 2.

a. what value for foot width is most frequent in males?
b. what is this value called?

1. determine the median value for foot width for males and for females. describe in complete sentences the method you used to determine the median values.
2. determine the mean for each data group, and describe in a complete sentence how you calculated them.

read this!
within a data set there may be individual values that seem uncharacteristic or do not fit the general trend. these data points may be referred to as outliers or anomalous data. in most samples, a small number of outliers is to be expected, due to the variation inherent in any naturally - occurring population. outliers can also result from errors in measurement or in the recording of data. normal variation can often be distinguished from error by repeating the measurements to see if the same range is obtained. scientists also use statistical calculations to determine the expected range of data, so that judgments can be made about the authenticity of individual data points. outliers should not be ignored, however, as many interesting scientific discoveries have resulted from the study of such unexpected findings.

Explanation:

Step1: Identify mode for male foot - width

For male foot - width values: 10, 10.5, 9, 9.3, 13, 7.5, 10, 9.2, 9, 4.5. Count the frequencies of each value. The value 10 appears 2 times, and other values appear less frequently.

Step2: Name the most frequent value

The most frequently occurring value in a data - set is called the mode.

Step3: Determine median for female foot - width

Arrange female foot - width values in ascending order: 5, 7, 7, 7.5, 7.5, 7.8, 7.8, 8, 8, 17. There are 10 values. The median is the average of the 5th and 6th ordered values. $\text{Median}=\frac{7.5 + 7.8}{2}=7.65$.

Step4: Determine median for male foot - width

Arrange male foot - width values in ascending order: 4.5, 7.5, 9, 9, 9.2, 9.3, 10, 10, 10.5, 13. There are 10 values. The median is the average of the 5th and 6th ordered values. $\text{Median}=\frac{9.2+9.3}{2}=9.25$.

Step5: Calculate mean for female foot - width

Sum of female foot - width values: $5 + 7+7+7.5+7.5+7.8+7.8+8+8+17 = 78.6$. There are 10 values. $\text{Mean}=\frac{78.6}{10}=7.86$.

Step6: Calculate mean for male foot - width

Sum of male foot - width values: $4.5+7.5 + 9+9+9.2+9.3+10+10+10.5+13 = 82$. There are 10 values. $\text{Mean}=\frac{82}{10}=8.2$.

Answer:

a. 10
b. Mode

1. Female median: 7.65. Arranged data in ascending order, as there are 10 values, took the average of 5th and 6th values. Male median: 9.25. Arranged data in ascending order, as there are 10 values, took the average of 5th and 6th values.
2. Female mean: 7.86. Calculated by summing all female foot - width values (78.6) and dividing by the number of values (10). Male mean: 8.2. Calculated by summing all male foot - width values (82) and dividing by the number of values (10).