Question

1. A question on a student survey asks: In a typical week, how many times do you eat at a fast food restaurant? The following data was then collected:

No. of times per week        No. of students

          5 or more                           2

          4                                       2

          3                                       3

          2                                       6

          1                                       0

          0                                       3

A. Find the mode (number of times per week) for this data.

B. Find the median (number of times per week) for this data.

C. Explain why you cannot compute the mean number of times per week using the data in the table.

2. A sample of n = 7 scores has a mean of 5. After one score is added to the sample, the new mean is found to be 7. What is the value of the new score? (Hint: compare the values for ∑X before and after the score is added.)

3. What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample.

4. Explain what it means to say that the sample variance provides an unbiased estimate of the population variance.

5. (Using both Excel and SPSS) For the following scores: 3, 1, 1, 1

1. Find the mean.
2. Find the variance (show your work).
3. Find the standard deviation.

6. (Using both Excel and SPSS) For the following scores: 1, 0, 4, 1, 1, 5

1. Find the mean.
2. Find the variance (show your work).
3. Find the standard deviation.

Answer 1

SOLUTIONS:

1)

A) The mode is most frequently data occur is 1.

B) So you list the number of times for each person in order...

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5+, 5+

Then you find the middle number. Since there's an even number, you find the average of the 2 middle numbers.

The median is 2

c) It could not continue mean number of times using the data in table due to the data are measured on a ratio scale.

2)

Given a sample n=7 scores has a mean of M=5.

The sample mean is,

If one person with X is added then the new is 35+X.

It is given that the new mean, M= 7.

The new sample size is 7+1=8.

The new score is,

Therefore, the new score is X = 21.

3.)

A standard deviation zero represents the there is no variably. In this case. all of the scores in the sample have exactly the same values.
4.)

It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.

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