Q 112. - The Practice of Statistics for AP

Question

Here are the heights (in centimeters) of 50 randomly selected Canadian students who participated in Census At School in 2007–2008: 

Make an appropriate graph to display these data. Describe the shape, center, and spread of the distribution. Are there any outliers? 

Step-by-Step Solution

Answer

Shape: symmetric and is not skewed.

Centre: $170 cm$

Spread: from $145.5$ which is the smallest value to $191$ which is the highest value.

Outliers: There are no outliers in the data

Step 1: Given information

Heights of $50$ randomly selected Canadian students.

Step 2: Concept

Statistical Measures are a descriptive-analytical technique that provides an overview of a data set's properties.

Step 3: Calculation

Shape: the dot-apex plot's is at $170$. It shows that the four students are all $170$ cm tall. As a result, the Mode is $170 cm$. The majority of the students are between the heights of $160$ and $180 cm$. The distribution is nearly symmetric and not skewed in any way.

The centre divides the observations into two equal sections, i.e. the median, such that about half of the observations take greater values and the other half take smaller values. The median height in this data is around $170cm (169.88cm)$

Spread: The spread of the distribution indicates the degree of variability in the data. Giving the greatest and smallest values is one technique to describe the dispersion. The range of the given data is$145.5$ to $191$, with $145.5$ being the lowest and$191$ being the highest. Instead, we can calculate range by subtracting the least and greatest values. The range would be$191-145.5 = 45.5cm$ in this case.

There are no outliers in the data, while there are several values, such as $143$ and $150$, that deviate from the overall pattern. They don't, however, stand out from the rest of the distribution.

Shape: symmetric and is not skewed.

Centre: $170 cm$

Spread: from $145.5$ which is the smallest value to $191$ which is the highest value.

Outliers: There are no outliers in the data