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.

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)

3. The groups are not equal because there are four men and one woman in the large bowl group and four women and one man in the small bowl group. Men and women differ in their food intake. This will naturally affect the result of the group.

This design flaw can be corrected by using a different technique to use the while making the group. the age group of the people selected hasn't been mentioned. So it isn't clear if the researcher factored that in too.

Group size could be having an even number of participants in both groups, with equal number from both sexes.

fichoh fichoh · Answer 2 · 2021-11-24T13:57:42+01:00

Using the data in the table given, the statistical values of each data can be calculated thus ;

Given the data:

Large Bowl:

424, 258, 376, 387, 445
Mean = 378
Standard deviation = 72.6

Small Bowl :

196, 274, 148, 202, 250
Mean = 214
Standard deviation = 49.3

1.)

Median of the large bowl :

Arrange values in ascending order :

258, 376, 387, 424, 445

Median = 1/2(n + 1)th term

Median = 1/2(6)th = 3rd term

Median = 387

2.)

Group with smaller range :

Range = maximum - minimum

Range(Large bowl) = 445 - 258 = 187

Range(Small bowl) = 274 - 148 = 126

3.)

The range, just like the standard deviation is a measure used to determine the spread of data in a distribution.

The small bowl has a lower range value, hence, a lower value of standard deviation.

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