Question

In: Statistics and Probability

26 randomly selected students were asked the number of movies they watched the previous week. The...

26 randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

# of Movies 0 1 2 3 4 5
Frequency 3 2 6 8 4 3



Round all your answers to one decimal place.

The mean is:

The median is:

The sample standard deviation is:

The first quartile is:

The third quartile is:

What percent of the respondents watched at least 4 movies the previous week? ______%

74% of all respondents watched fewer than how many movies the previous week?

Solutions

Expert Solution

(a)

From the given data, the following Table is calculated:

x f f.x f.x2 cf
0 3 0 0 3
1 2 2 2 5
2 6 12 24 11
3 8 24 72 19
4 4 16 64 23
5 3 15 75 26
Total = n = 26

Mean () is given by:

(b)

Median is (26/2)th item = 13th item.

From the column of Cumulative Frequency, cf, we note, 13th item = 3.

So,

Median = 3

(c)

Sample Standard Deviation (s) is given by:

So,

Sample Standard Deviation = 1.4681

(d)

First Quartile = Q1 = (27/4)th item = 6.75th item = 2

So,

First Quartile = Q1 = 2

(e)

Third Quartile = Q1 = (27 X 3/4)th item = 20.25th item = 4

So,

Third Quartile = Q3 = 4

(e)

Percentage of respondents at least 4 movies = [ (4 + 3)/26 ] X 100 = 26.92%

So,

Percentage of respondents at least 4 movies = 26.92%

(f)

74% of all respondents watched fewer than the number of movies the previous week = 74th percentile

= 26 X 74/100th item = 19.24th item

From the column of Cumulative Frequency, cf, we note, 19.24th item = 4

So,

74% of all respondents watched fewer than the number of movies the previous week is:

4


Related Solutions

27 randomly selected students were asked the number of movies they watched the previous week. The...
27 randomly selected students were asked the number of movies they watched the previous week. The results are as follows: # of Movies 0 1 2 3 4 5 6 Frequency 5 2 2 3 7 3 5 Round all your answers to 4 decimal places where possible. The mean is: The median is: The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents watched at least 6 movies the previous week?...
22 randomly selected students were asked the number of movies they watched the previous week. The...
22 randomly selected students were asked the number of movies they watched the previous week. The results are as follows: # of Movies 0 1 2 3 4 5 6 Frequency 4 1 1 5 6 3 2 Round all your answers to 4 decimal places where possible. The mean is: The median is: The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents watched at least 2 movies the previous week?...
Fifty randomly selected students were asked the number of movies they watched them previous week. The...
Fifty randomly selected students were asked the number of movies they watched them previous week. The results are as follows: # of Movies # of Movies | Student Frequency 0. 10 1 . 18 2 . 12 3 . 8 4 . 2 a) Find the sample mean, median, and range of the sample. . b) Find the standard deviation and the variance. c) Find the first quartile. (1 mark) d) Find the second quartile. To which value it corresponds?...
Randomly selected students in a statistics class were asked to report the number of hours they...
Randomly selected students in a statistics class were asked to report the number of hours they slept on weeknights and on weekends. At α = 0.05. Can it be claimed that the scores on 2 tests are correlated on 0.01 significance level? Student #: 1 2 3 4 5 6 7 8 Test 1: 67 88 76 88 91 95 79 71 Test 2: 69 78 76 84 86 96 70 68
Fifteen randomly selected college students were asked to state the number of hours they slept the...
Fifteen randomly selected college students were asked to state the number of hours they slept the previous night. The resulting data are 5, 10, 7, 8, 6, 7, 7, 6, 6, 9, 4, 3, 8, 9, 7. Find the following. (Round your answers to two decimal places.) (a) Variance s2, using formula below $ s^2 = \dfrac{\sum{(x - \overline{x})^2}}{n - 1}$ s2 = (b) Variance s2, using formula $ s^2 = \dfrac{\sum{x^2} - \dfrac{(\sum{x})^2}{n}}{n - 1} $ s2 = (c)...
Measures of Center and Spread 64 randomly selected students were asked the number of pairs of...
Measures of Center and Spread 64 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows: # of Pairs of Shoes 4 5 6 7 8 9 10 11 Frequency 11 6 6 9 9 8 9 6 Round all your answers to 4 decimal places where possible. The mean is: ____ The median is: ___ The sample standard deviation is: ____ The...
59 randomly selected students were asked the number of pairs of shoes they have. Let X...
59 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows: Round all your answers to 4 decimal places where possible. The mean is: The median is: The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents have at least 12 pairs of Shoes? % 53% of all respondents have fewer than how many pairs...
Fifty randomly selected students were asked the number of speeding tickets they have had. The results...
Fifty randomly selected students were asked the number of speeding tickets they have had. The results are as follows: Tickets Frequency 0 8 1 15 2 21 3 3 4 2 5 0 6 1 Round your answers to two decimal places. The mean is: The median is:                             The sample standard deviation is:    The first quartile is: The third quartile is:                               What...
64 randomly selected students were asked the number of pairs of shoes they have. Let X...
64 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows: # of Pairs of Shoes 4 5 6 7 8 9 10 11 12 13 14 15 Frequency 4 4 3 7 2 5 10 5 5 8 6 5 Round all your answers to 4 decimal places where possible. The mean is: The median is: The sample standard deviation is: The...
57 randomly selected students were asked the number of pairs of shoes they have. Let X...
57 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows: # of Pairs of Shoes 4 5 6 7 8 9 10 11 Frequency 7 8 14 4 3 4 7 10 Round all your answers to 4 decimal places where possible. The mean is: __________________ The median is: __________________ The sample standard deviation is: __________________ The first quartile is: __________________ The...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT