Q. 112 - The Practice of Statistics for AP

Question

How tall are you? (1.2) Here are the heights (in centimetres) of $50$ randomly selected Canadian students who participated in CensusAtSchool in :

 

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

Step-by-Step Solution

Answer

The shapes of ranges are approximately symmetric, the centre is roughly at $170$, the spread range is between $145$ and $195$ and there are no outliers.

Step 1: The Given data

The below chart displays the heights of $50$ randomly selected Canadian students who participated in CensusAtSchool in $2007-2008$.

Step 2: The bar graph to display data

The sample is very large and the variables are quantitative. Therefore, it will be better to make a histogram of the given data.

The width of the bars is to be equal, while the height is to be equal to the frequency.

Step 3:Determination of the shape

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

Step 4: Calculation for centre

Centre: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 in this data is around $170 cm$($169.88 cm$).

Step 5: Calculation for spread

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 $191-145.5=45.5 \mathrm{cm}$,$145.5cm$ being the lowest and 191 being the highest. Instead, we can calculate range by subtracting the least and greatest values. 

Step 6:Calculation for outliners

Outliners: 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.