A cereal company is determining the nutritional information of a new recipe. They took a random sample of 20 servings of the cereal and measured
the number of calories in each serving. The number of calories in each serving are listed.
143, 145, 147, 150, 150, 152, 157, 159, 160, 160, 161, 163, 164, 165, 165, 168, 173, 175, 177, 180
The box plot shown is a summary of the data. Move numbers to the spaces to label the values and complete the box plot.
143
180
not drawn to sale
145
150
151
160.5
160.7
165
166.5
177

The first box is fillled with first quartile 151, the second box is filled with second quartile 160.5, and the third box is filled with the third quartile 166.5

How does a boxplot shows the data points?

A box plot has 5 data description.

The leftmost whisker shows the minimum value in the data.
The rightmost whisker shows the maximum value in the data.
The leftmost line in the box shows the first quartile.
The middle line shows the median, also called second quartile.
The last line of the box shows the third quartile.

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Similarly, second quartile (also called median) is approximately in mid of the data.

Third quartile (also called upper quartile) has approx 75% in its left partition, and on its right lies approx 25% of the data.

Left to right is said in assumption that data was arranged increasingly from left to right

For this case, the data is:

143, 145, 147, 150, 150, 152, 157, 159, 160, 160, 161, 163, 164, 165, 165, 168, 173, 175, 177, 180

It is already sorted. There are 20 values.

We have to find the limits of box and the mid line, which are the three quartiles.

Dividing 20 in 4 equal parts give size of 5

Thus, 5-5-5-5 groups will be made by the three quartiles of this data.

The fifth value is 150, and sixth is 152. Any number between 150 and 152 can be taken as the first quartile, as before it will lie 25% of values and 75% of the data after that value. By tradition, we take average of these two values, so its 151 as the first quartile of the considered data set.

In the similar way, the second quartile or median is mean of 10th and 11th value which evaluates to (160+161)/2 = 160.5

And, the third quartile is the mean of 15th and 16th value of this data set, which evaluates to (165+168)/2 = 166.5

Thus, the first box is fillled with first quartile 151, the second box is filled with second quartile 160.5, and the third box is filled with the third quartile 166.5

Learn more about quartiles here:

brainly.com/question/9260741