Question

task: find the measure of center for the height of the students
a. find mean:__ median: mode: range: sd:__
b. find the five - number summary for the height of the students
min:__ q1: median: q3: max:__
interquartile range:____ q3 - q1
lower outlier:____=q1-(1.5)(iqr)
upper outlier:____=q3+(1.5)(iqr)

Explanation:

Step1: Organize data

First, arrange the student - height data in ascending order.

Step2: Calculate mean

Sum all the height values and divide by the number of students. Let the heights be \(x_1,x_2,\cdots,x_n\), then the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\).

Step3: Calculate median

If \(n\) is odd, the median is the middle - value. If \(n\) is even, the median is the average of the two middle - values.

Step4: Calculate mode

The mode is the most frequently occurring height value.

Step5: Calculate five - number summary

The minimum (Min) is the smallest height value. The first quartile \(Q1\) is the median of the lower half of the data. The median (already calculated) is the second quartile. The third quartile \(Q3\) is the median of the upper half of the data. The maximum (Max) is the largest height value.

Step6: Calculate inter - quartile range (IQR)

\(IQR = Q3 - Q1\).

Step7: Calculate lower and upper outliers

Lower Outlier \(=Q1-(1.5)\times IQR\), Upper Outlier \(=Q3+(1.5)\times IQR\).

Step8: Calculate range

Range \(=\text{Max}-\text{Min}\).

Step9: Calculate standard deviation (SD)

The formula for the sample standard deviation is \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\).

Answer:

The values of mean, median, mode, five - number summary (Min, Q1, Median, Q3, Max), inter - quartile range, lower and upper outliers, range, and standard deviation will be obtained after performing the above calculations on the actual student - height data.