Question

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:Number of Movies Frequency0 51 92 63 44 1Round your answers to two decimal places.a. The mean is: _____b. The median is: _____c. The sample standard deviation is: _____d. The first quartile is: _____e. The third quartile is: _____f. What percent of the respondents watched at least 3 movies the previous week?g. 56% of all respondents watched at fewer than how many movies the previous week?

Answer 1

Answer:

a) M = 1.48

b) Median = 2

c) $\sigma = 1.12$

d) Q1 = 1

e) Q3 = 2

f) 20%

g) 56% of all respondents watched fewer than 2 movies

Step-by-step explanation:

So, the following relation:

Number of movies - Frequency

0 - 5

1 - 9

2 - 6

3 - 4

4 - 1

Our set is = {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,4}

a) The mean is the sum of each number of movies watched multiplied by it's frequencies divided by the sum of the frequencies. So

$M = \frac{5*0 + 1*9 + 2*6 + 3*4 + 4*1}{5 + 9 + 6 + 4 + 1}$

$M = \frac{37}{25}$

$M = 1.48$

b) The number of movies watched is a set with odd(N=25) cardinality. So the median of the set will be element at the position (N+1)/2 = 13, which is 1.

c) The sample standard deviation of a sample is given by the following formula:

$\sigma = \sqrt{\frac{1}{N} \sum_{k=1}^{N} (x_{i} - M)^2}$

where $x_{i}$ is the element at the position i of the set and M is the mean of the set.

So for this question, $\sigma = 1.122$

d) The first quartile is the median of the lower half of the data set.

It will be the term of the set at following position P

$P = \frac{(N+1)}{4} = \frac{26}{4} = 6.5$

So the first quartile is the average between the elements at the 6th and 7th position. Both are 1, so first quartile = 1

e) The third quartile is the median of the upper half of the data set.

It will be the term of the set at following position P

$P = \frac{3(N+1)}{4} = \frac{78}{4} = 19.5$

So the third quartile is the average between the elements at the 19th and 20th position. Both are two, so Q3 = 2.

f) Out of 25 people, 4 watched 3 movies and and 1 watched four movies. So five people watched at least 3 movies, out of 25. 5/25 = 20% of the respondents watched at least 3 movies the previous week

g) 0.56*25 = 14 people watched at most 1 movie. So 56% of all respondents watched fewer than 2 movies.

Answer 2

The mean of the data set is 1.48, the median of the given data is 1, the sample standard deviation of the given data is 1.122, the first quartile is 1, the third quartile is 2, the percent of the respondents who watched at least 3 movies the previous week is 20%, and 56% of all respondents watched fewer than 2 movies.

Given :

Twenty-five randomly selected students were asked the number of movies they watched the previous week.

The results are as follows:

Number of Movies           Frequency

           0                                  5

           1                                   9

           2                                  6

           3                                   4

           4                                   1

a) Mean of the data set is given by:

$\rm M = \dfrac{(5\times 0)+(1\times 9)+(2\times 6)+(3 \times 4)+(4\times 1)}{5+9+6+4+1}$

$\rm M =\dfrac{37}{25}$

M = 1.48

b) The median of the given data is:

$\rm \dfrac{N+1}{2}=\dfrac{25+1}{2}=13$

So, the median is 1.

c) The sample standard deviation of the given data is:

$\rm \sigma = \sqrt{\dfrac{1}{N}\times \sum^N_{K=1}(x_i-M)^2}$

Now, substitute the values of known terms in the above formula and then simplify it in order to get the value of standard deviation.

$\sigma = 1.122$

d) The first quartile is given by:

$\rm P = \dfrac{N+1}{4}=\dfrac{26}{4}=6.5$

So, the first quartile is in between 6th and 7th position. Therefore, the value of the first quartile is 1.

e) The third quartile is given by:

$\rm P = \dfrac{3(N+1)}{4}=\dfrac{3\times 26}{4}=19.5$

So, the third quartile is in between 19th and 20th position. Therefore, the value of the third quartile is 2.

f) The percent of the respondents who watched at least 3 movies the previous week is given by:

$=\dfrac{5}{25}\times 100$

= 20%

g) 0.56 $\times$ 25 = 14

14 people watched one movie. Therefore, 56% of all respondents watched fewer than 2 movies.

For more information, refer to the link given below:

https://brainly.com/question/23044118