Question

AP Exam Practice:

Researchers conducted a study in which 10 participants went to a laboratory around dinner time. The researcher assigned students to one of two groups by flipping a coin. Half of the participants were assigned to a “large bowl” group, and half were assigned to a “small bowl” group. By luck of the draw, 4 men and 1 woman were in the “large bowl” group, and 4 women and 1 man were in the “small bowl” group. Participants were told they could take as much pasta as they wanted from the serving bowl in the middle of the table, which was kept at nearly a full level. Participants were encouraged to go back for as many helpings of pasta as they wanted. In order to determine how much food each participant actually ate, the researchers measured the weight of the food that each participant took, as well as the amount that the participants left in the bowls.

The amount of pasta (in grams) each participant ate is shown in the table below:

Large Bowl
Small Bowl
424
258
376
387
445
196
274
148
202
250
Mean: 378
Mean: 214
Std. Dev.: 72.6
Std. Dev.: 49.3

Part A:
Determine the median of the “large bowl” group. 387 because it the median large bowl,


Which group has a smaller range?

Explain how the smaller range related to the standard deviation.


Convert this frequency distribution table into a chart. (Correctly label the x and y axis)

Answer 1

Median: 387

small bowl.

Range is related to standard deviation. Smaller the range smaller is the standard deviation

Histogram is attached.

Step-by-step explanation:

The table is attached.

Arranging the data of large bowl in ascending order :

258, 376, 387, 424, 445

Median: 387

Range of large bowl: 187

Range of small bowl: 126

small bowl has smaller range

The range and standard deviation are both related by range rule. The range rule says standard deviation is approximately equal to one-fourth of the range.

The frequency distribution chart in the form of histogram is attached