Question

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?

Answer 1

(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:

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