4. the dotplot shows the number of calories per serving for 16 brands of frozen cheese pizza. a. identify…

4. the dotplot shows the number of calories per serving for 16 brands of frozen cheese pizza. a. identify any outliers in the distribution. b. give the five - number summary. minimum $q_1$ median $q_3$ maximum c. make a boxplot.

4. the dotplot shows the number of calories per serving for 16 brands of frozen cheese pizza. a. identify any outliers in the distribution. b. give the five - number summary. minimum $q_1$ median $q_3$ maximum c. make a boxplot.

Answer

Explanation:

Step1: Arrange data in ascending order

The data points from the dot - plot are: 260, 320, 320, 320, 330, 330, 340, 340, 340, 350, 350, 360, 360, 380, 400.

Step2: Find the minimum and maximum

The minimum value is 260 and the maximum value is 400.

Step3: Calculate the median

Since (n = 16) (even), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+ 1))th ordered values. (\frac{n}{2}=8) and (\frac{n}{2}+1 = 9). The 8th value is 340 and the 9th value is 340, so the median (Q_2=\frac{340 + 340}{2}=340).

Step4: Calculate (Q_1)

The lower half of the data is the first 8 values. Since (n_1 = 8) (even), (Q_1) is the average of the (\frac{n_1}{2})th and ((\frac{n_1}{2}+1))th ordered values of the lower - half data. The 4th value of the lower - half data is 320 and the 5th value is 330, so (Q_1=\frac{320+330}{2}=325).

Step5: Calculate (Q_3)

The upper half of the data is the last 8 values. Since (n_2 = 8) (even), (Q_3) is the average of the (\frac{n_2}{2})th and ((\frac{n_2}{2}+1))th ordered values of the upper - half data. The 4th value of the upper - half data is 350 and the 5th value is 360, so (Q_3=\frac{350 + 360}{2}=355).

Step6: Check for outliers

The inter - quartile range (IQR=Q_3 - Q_1=355 - 325 = 30). The lower fence is (Q_1-1.5\times IQR=325-1.5\times30=325 - 45 = 280). The upper fence is (Q_3 + 1.5\times IQR=355+1.5\times30=355 + 45 = 400). The value 260 is less than 280, so 260 is an outlier.

Answer:

a. The outlier is 260. b.

Minimum (Q_1) Median (Q_3) Maximum
260 325 340 355 400
c. To make a box - plot:
  1. Draw a number line that includes the range from 260 to 400.
  2. Draw a box from (Q_1 = 325) to (Q_3=355).
  3. Draw a vertical line inside the box at the median (Q_2 = 340).
  4. Draw whiskers from the box to the minimum (260) and maximum (400) non - outlier values. Mark the outlier 260 with a dot.